{"id":2831,"date":"2021-07-23T11:09:09","date_gmt":"2021-07-23T05:39:09","guid":{"rendered":"http:\/\/ncertsolutions.guru\/?p=2831"},"modified":"2021-07-23T15:10:28","modified_gmt":"2021-07-23T09:40:28","slug":"ncert-solutions-for-class-9-maths-chapter-7-hindi","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium)"},"content":{"rendered":"

NCERT Solutions for Class 9 Maths Chapter 7 Triangles (\u0924\u094d\u0930\u093f\u092d\u0941\u091c) (Hindi Medium)<\/span><\/h2>\n

These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium<\/a>. Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles.<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.1<\/strong><\/span><\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ACBD \u092e\u0947\u0902, AC = AD \u0939\u0948 \u0914\u0930 \u00a0AB, \u2220A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 | (see Fig.). \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0394ABC \u2245 \u0394ABD \u0939\u0948|<\/strong>
\n\u0939\u0932:<\/strong>
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0AC = AD \u0914\u0930 AB \u2220A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948|
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e\u00a0:\u00a0<\/strong>\u00a0\u0394 ABC \u2245 \u0394 ABD.
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>
\n\u0394 ABC \u0924\u0925\u093e \u0394ABD \u092e\u0947\u0902,
\nAC = AD [\u0926\u093f\u092f\u093e \u0939\u0948]
\n\u2220CAB = \u2220BAD [AB \u2220A\u00a0\u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u00a0]
\nAB = AB [\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920]
\nSAS\u00a0\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 ABC \u2245 \u0394 ABD
\nBC = BD [CPCT]<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AD = BC \u0939\u0948 \u0914\u0930 \u2220 DAB = \u2220 CBA\u00a0(see Fig.) \u0939\u0948|\u00a0\u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f :\u00a0<\/strong>
\n(i) \u0394 ABD \u2245 \u0394 BAC<\/strong>
\n(ii) BD = AC<\/strong>
\n(iii) \u2220 ABD = \u2220 BAC \u00a0 \u00a0 \u00a0 \u00a0<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AD = BC \u0914\u0930 \u2220 DAB = \u2220 CBA \u00a0\u0939\u0948|
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948\u00a0<\/strong>:
\n\"Maths
\n(i) \u0394 ABD \u2245 \u0394 BAC
\n(ii) BD = AC
\n(iii) \u2220 ABD = \u2220 BAC
\n\u092a\u094d\u0930\u092e\u093e\u0923\u00a0<\/strong>:
\n(i) \u0394 ABD \u0924\u0925\u093e\u00a0\u0394 BAC \u092e\u0947\u0902,
\nAD = BC [\u0926\u093f\u092f\u093e \u0939\u0948]
\n\u2220 DAB = \u2220 CBA\u00a0\u00a0 [\u0926\u093f\u092f\u093e \u0939\u0948]
\nAB = AB [\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920]
\nSAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 ABD \u2245 \u0394 BAC
\n(ii)\u00a0\u00a0BD = AC\u00a0[By CPCT]
\n(iii)\u00a0\u2220 ABD = \u2220 BAC\u00a0[By CPCT]<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u090f\u0915 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 AB \u092a\u0930 AD \u0914\u0930 BC \u0926\u094b \u092c\u0930\u093e\u092c\u0930 \u0932\u0902\u092c \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u092f\u0947 \u0906\u0915\u0943\u0924\u093f)| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f CD, AB \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948|
\n\"Class
\n<\/strong><\/p>\n

\u0939\u0932 :
\n<\/strong>\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0AD \u22a5 AB \u0914\u0930 BC\u00a0\u22a5 AB \u0939\u0948 \u0914\u0930 AD = BC \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :
\nAO = BO \u0905\u0930\u094d\u0925\u093e\u0924\u00a0CD, AB \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :
\n\u2206AOD\u00a0\u0924\u0925\u093e\u00a0\u2206BOC
\n\u2220AOD\u00a0=\u00a0\u2220 BOC\u00a0(\u0936\u0940\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u2220DAO\u00a0=\u00a0\u2220CBO\u00a0\u00a0(\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 90\u00ba)
\nBC = AD (\u0926\u093f\u092f\u093e \u0939\u0948)
\nASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u2206AOD\u00a0\u2245\u200b\u00a0\u2206BOC
\n\u2234 \u00a0AO = BO \u00a0 (By CPCT)
\n\u0905\u0924:\u00a0CD, AB \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0l<\/em>\u00a0\u0914\u0930 m \u0926\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u0930\u0947\u0916\u093e\u090f\u0901 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0938\u092e\u093e\u0902\u0924\u0930 \u0930\u0947\u0916\u093e\u0913\u0902 p \u0914\u0930 q \u0915\u093e \u090f\u0915 \u0905\u0928\u094d\u092f \u092f\u0941\u0917\u094d\u092e \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u093e \u0939\u0948| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u2206ABC \u2245 \u2206CDA\u00a0\u0939\u0948|
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n<\/strong>\u0926\u093f\u092f\u093e \u0939\u0948 :l<\/em>\u00a0|| m \u0914\u0930 p || q \u0939\u0948 \u091c\u094b \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b A, B, C \u00a0\u0924\u0925\u093e D \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0\u2206ABC \u2245 \u2206CDA
\n\u092a\u094d\u0930\u092e\u093e\u0923 :
\nl<\/em>\u00a0|| m …….. (1) \u00a0\u0926\u093f\u092f\u093e \u0939\u0948 |
\np || q \u00a0………(2) \u00a0\u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u0938\u092e\u0940\u0966 (1) \u0924\u0925\u093e (2) \u0938\u0947
\nABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0905\u092c,\u00a0\u2206ABC \u0924\u0925\u093e \u2206CDA \u092e\u0947\u0902,
\nBC = AD \u00a0[\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e ]
\n\u2220B =\u00a0\u2220D \u00a0[\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 ]
\nAC = AC \u00a0[\u0926\u093f\u092f\u093e \u0939\u0948 ]
\nSAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u2234\u00a0 \u00a0\u2206ABC \u2245 \u2206CDA
\nProved.<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u0930\u0947\u0916\u093e\u00a0l\u00a0<\/em>\u0915\u094b\u0923 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0914\u0930 B \u0930\u0947\u0916\u093e\u00a0l<\/em>\u00a0\u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948 | BP \u0914\u0930 BQ \u0915\u094b\u0923 A \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 B \u0938\u0947 \u0921\u093e\u0932\u0947 \u0917\u090f \u0932\u092e\u094d\u092c \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u092f\u0947 \u0906\u0915\u0943\u0924\u093f 7.20) \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f :<\/strong>
\n(i)\u00a0\u0394 APB \u2245 \u0394 AQB<\/strong>
\n(ii)\u00a0BP = BQ \u0939\u0948\u0902, \u0905\u0930\u094d\u0925\u093e\u0924 \u092c\u093f\u0902\u0926\u0941 B \u0915\u094b\u0923 \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u00a0<\/strong>
\n\"NCERT
\n\u0939\u0932: <\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u2220PAQ \u0915\u094b \u0930\u0947\u0916\u093e\u00a0l\u00a0<\/em><\/strong>\u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0914\u0930 BP \u0924\u0925\u093e BQ, AP \u0924\u0925\u093e AQ \u092a\u0930 \u0915\u094d\u0930\u092e\u0936: \u0932\u0902\u092c \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n(i) \u0394 APB \u2245 \u0394 AQB
\n(ii) BP = BQ
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>
\n(i) \u0394 APB \u0924\u0925\u093e \u0394 AQB \u092e\u0947\u0902,
\n\u2220APB = \u2220AQB \u00a0(90\u0966<\/sup>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915)
\n\u2220PAB =\u00a0\u2220QAB \u00a0(\u0926\u093f\u092f\u093e \u0939\u0948)
\nAB = AB (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 APB \u2245 \u0394 AQB
\n\u2234\u00a0\u00a0(ii) BP = BQ (By CPCT)<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6. \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902,\u00a0AC = AE, AB = AD \u0914\u0930\u00a0\u2220 BAD = \u2220 EAC \u0939\u0948| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0BC = DE \u0939\u0948|\u00a0<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>AC = AE, AB = AD \u0914\u0930\u00a0\u2220 BAD = \u2220 EAC \u0939\u0948|
\n\"NCERT
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>BC = DE
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>
\n\u2220 BAD = \u2220 EAC \u00a0 ……… (1) \u0926\u093f\u092f\u093e \u0939\u0948
\n\u0938\u092e\u0940\u0966 \u0915\u0947 \u00a0\u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u092e\u0947\u0902\u00a0\u2220 CAD\u00a0\u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u2220 BAD +\u00a0\u2220 CAD\u00a0= \u2220 EAC +\u00a0\u2220 CAD
\n\u092f\u093e \u00a0\u2220 BAC = \u2220 EAD \u00a0 ……. (2)
\n\u0394 BAC \u0924\u0925\u093e \u0394 DAE \u092e\u0947\u0902
\nAC = AE (\u0926\u093f\u092f\u093e \u0939\u0948)
\nAB = AD (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220 BAC = \u2220 EAD ……[\u0938\u092e\u0940\u0966 (2) \u0938\u0947]
\nSAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 BAC \u2245 \u0394 DAE
\n\u2234 BC = DE \u00a0 (By CPCT)
\nProved.<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q7. AB \u090f\u0915 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0939\u0948 \u0914\u0930 P \u0907\u0938\u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 | D \u0914\u0930 E \u0930\u0947\u0916\u093e\u0916\u0902\u0921 AB \u0915\u0947 \u090f\u0915 \u0939\u0940 \u0913\u0930 \u0938\u094d\u0925\u093f\u0924 \u0926\u094b \u092c\u093f\u0902\u0926\u0941 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902 \u0915\u093f\u00a0\u2220 BAD = \u2220 ABE \u0914\u0930\u00a0\u2220 EPA = \u2220 DPB \u0939\u0948 | (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f 7.22) |\u00a0<\/strong>
\n\"NCERT
\n\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f :\u00a0<\/strong>
\n(i) \u0394 DAP \u2245 \u0394 EBP
\n(ii) AD = BE<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0AB \u090f\u0915 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0939\u0948 \u0914\u0930 P \u0907\u0938\u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948|
\n\u2220 BAD = \u2220 ABE \u0914\u0930\u00a0\u2220 EPA = \u2220 DPB \u0939\u0948|
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n(i) \u0394 DAP \u2245 \u0394 EBP
\n(ii) AD = BE
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>
\n\u2220 EPA = \u2220 DPB \u00a0 \u00a0…..(1)\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u0938\u092e\u0940\u0966 (1) \u0915\u0947 \u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u092e\u0947\u0902\u00a0\u2220 EPD \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u2220 EPA +\u00a0\u2220 EPD\u00a0= \u2220 DPB +\u00a0\u2220 EPD
\n\u092f\u093e\u00a0\u00a0\u2220 DPA =\u00a0\u2220 EPB \u00a0 \u00a0……… (2)
\n(1)\u00a0\u0394 DAP \u0924\u0925\u093e \u0394 EBP \u092e\u0947\u0902
\nAP = BP \u00a0…….\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220 BAD = \u2220 ABE \u00a0..(\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220 DPA =\u00a0\u2220 EPB \u00a0 \u00a0….[\u0938\u092e\u0940\u0966 (2) \u0938\u0947]
\nASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 DAP \u2245 \u0394 EBP
\n(ii) AD = BE\u00a0(BY CPCT)<\/p>\n

Ex 7.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q8. \u0938\u0902\u0932\u0917\u094d\u0928 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092e\u0947\u0902, \u091c\u093f\u0938\u092e\u0947\u0902 \u2220C \u0938\u092e\u0915\u094b\u0923 \u0939\u0948, M \u0915\u0930\u094d\u0923 AB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948\u0964 C \u0915\u094b M \u0938\u0947 \u092e\u093f\u0932\u093e\u0915\u0930 D \u0924\u0915 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0922\u093c\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f DM = CM \u0939\u0948\u0964 \u092c\u093f\u0928\u094d\u0926\u0941 D \u0915\u094b \u092c\u093f\u0928\u094d\u0926\u0941 B \u0938\u0947 \u092e\u093f\u0932\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i) \u2206AMC = \u2206BMD<\/strong>
\n(ii) \u2220DBC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0939\u0948\u0964<\/strong>
\n(iii) \u2206DBC = \u2206ACB<\/strong>
\n(iv) GM = \\(\\frac { 1 }{ 2 }\\) AB<\/strong>
\n\"Maths
\n\u0939\u0932-<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948: ABC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u2220C = 90\u00b0 \u0939\u0948 \u0924\u0925\u093e \u0915\u0930\u094d\u0923 AB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948\u0964 M \u0939\u0948\u0964 \u0930\u0947\u0916\u093e\u0916\u0923\u094d\u0921 CM \u0916\u0940\u0902\u091a\u0915\u0930 \u0907\u0938\u0947 \u092c\u093f\u0928\u094d\u0926\u0941 D \u0924\u0915 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0922\u093c\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f CM = DM \u0939\u0948\u0964 \u092c\u093f\u0928\u094d\u0926\u0941 D \u0915\u094b \u092c\u093f\u0928\u094d\u0926\u0941 B \u0938\u0947 \u092e\u093f\u0932\u093e\u0915\u0930 \u0930\u0947\u0916\u093e BD \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0939\u0948\u0964
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) \u2206AMC = \u2206BMD
\n(ii) \u2220DBC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0939\u0948\u0964
\n(iii) \u2206DBC = \u2206ACB
\n(iv) GM = \\(\\frac { 1 }{ 2 }\\) AB
\n\u0909\u092a\u092a\u0924\u094d\u0924\u093f :<\/strong>
\n(i) \u2206AMC \u0914\u0930 \u2206BMD \u092e\u0947\u0902, AM = BM (M, AB \u0915\u093e \u092e\u0927\u094d\u092f \u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948)
\nCM = DM (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220AMC = \u2220BMD (\u0930\u0947\u0916\u093e\u0916\u0923\u094d\u0921\u094b\u0902 AB \u0914\u0930 CD \u0915\u0947 \u0915\u093e\u091f\u0928\u0947 \u0938\u0947 \u092c\u0928\u0947 \u0936\u0940\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923 \u0939\u0948\u0902)
\n\u2206AMC = \u2206BMD (\u092d\u0941\u091c\u093e-\u0915\u094b\u0923-\u092d\u0941\u091c\u093e \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0938\u0947)
\n(ii, iii). \u2206AMC = \u2206BMD
\nAC = BD \u0924\u0925\u093e AM = DM \u0914\u0930 CM = BM (\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0917\u0924 \u092d\u0941\u091c\u093e\u090f\u0901)
\nAM = DM ……(1)
\nBM = CM …… (2)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0935 (2) \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u092a\u0930\u0964
\nAM + BM = CM + DM
\nAB = CD [AB = AM + BM \u0924\u0925\u093e CM + DM = CD]
\n\u0905\u092c, \u2206ACB \u0914\u0930 \u2206DBC \u092e\u0947\u0902,
\nAC = BD (\u2206AMC \u0914\u0930 \u2206BMD \u0915\u0940 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0938\u0947)
\nAB =CD (\u090a\u092a\u0930 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e \u091a\u0941\u0915\u093e \u0939\u0948)
\nBC = BC (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u2206ACB = \u2206DBC (\u092d\u0941\u091c\u093e-\u092d\u0941\u091c\u093e-\u092d\u0941\u091c\u093e \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0938\u0947)
\n\u0905\u092c \u2206ACB = \u2206DBC
\n\u2220DBC = \u2220ACB (\u090f\u0915\u093e\u0928\u094d\u0924\u0930 \u0915\u094b\u0923)
\n\u092a\u0930\u0928\u094d\u0924\u0941 \u0926\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u2220ACB \u092f\u093e \u2220C = 90\u00b0
\n\u2220DBC = 90\u00b0
\n\u0905\u0924\u0903 \u2220DBC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0939\u0948\u0964
\n(iv) \u0926\u093f\u092f\u093e \u0939\u0948 \u0915\u093f M, AB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948\u0964
\nAM = BM \u0914\u0930 AM + BM = AB
\n\u0905\u092c AM + BM = AB
\nAM + AM = AB (BM \u0915\u0947 \u0938\u094d\u0925\u093e\u0928 \u092a\u0930 AM \u0930\u0916\u0928\u0947 \u092a\u0930)
\n2 AM = AB …….(3)
\n\u092a\u0930\u0928\u094d\u0924\u0941 \u2206ACB = \u2206DCB
\nAB = CD
\n\\(\\frac { 1 }{ 2 }\\) AB = \\(\\frac { 1 }{ 2 }\\) CD
\nAM = CM … (4)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (3) \u0935 (4) \u0938\u0947
\n2CM = AB
\nCM = \\(\\frac { 1 }{ 2 }\\) AB
\n\u0907\u0924\u093f \u0938\u093f\u0926\u094d\u0927\u092e.<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.2<\/strong><\/span><\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924 Q1. \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092e\u0947\u0902 \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948, \u2220B \u0914\u0930 \u2220C \u0915\u0947 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u092a\u0930\u0938\u094d\u092a\u0930 \u092c\u093f\u0902\u0926\u0941 O \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902| A \u0914\u0930 O \u0915\u094b \u091c\u094b\u0921\u093f\u090f | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f :<\/strong>
\n(i) OB = OC<\/strong>
\n(ii) AO \u0915\u094b\u0923\u00a0\u2220 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |\u00a0<\/strong>
\n\"Maths
\n\u0939\u0932:\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948: \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/strong>\u00a0ABC \u092e\u0947\u0902, \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC,\u00a0\u00a0\u0914\u0930 \u2220 B \u0914\u0930 \u2220 C \u0915\u094b\u0923 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 O \u092a\u0930 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) OB = OC
\n(ii) AO \u0915\u094b\u0923 \u2220 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>\u00a0\u0394ABC \u092e\u0947\u0902 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u0948:
\nAB = AC
\n\u2220 B = \u2220 C [ \u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 | ]
\n\u0905\u0925\u0935\u093e\u00a0 \\(\\frac { 1 }{ 2 }\\) \u2220 B = \\(\\frac { 1 }{ 2 }\\) \u2220C
\n\u0907\u0938\u0932\u093f\u090f, \u2220OBC = \u2220OCB [\u20261]
\n\u0394ABO and\u00a0\u0394ACO \u092e\u0947\u0902
\nAB = AC [\u0926\u093f\u092f\u093e \u0939\u0948 ]
\n\u2220OBC = \u2220OCB [\u0938\u092e\u09400 1 \u0938\u0947\u00a0]
\nAO = AO [\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920]
\nSAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABO\u00a0\u2245\u00a0\u00a0\u0394ACO
\nOB = OC [ By CPCT ]
\n\u2220BAO = \u2220CAO [ By CPCT ]
\n\u0905\u0924: AO \u0915\u094b\u0923 \u2220A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2.\u00a0\u0394 ABC \u092e\u0947\u0902, AD \u092d\u0941\u091c\u093e BC \u0915\u093e \u0932\u092e\u094d\u092c \u0938\u092e\u094d\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948 (\u0926\u0947\u0916\u093f\u092f\u0947 \u0906\u0915\u0943\u0924\u093f). \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0\u0394 ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902\u00a0AB = AC \u0939\u0948|.<\/strong>
\n\"Maths
\n\u0939\u0932:<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>\u0394 ABC \u092e\u0947\u0902, AD, BC \u0915\u093e \u0932\u0902\u092c \u0938\u092e\u094d\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948 |.
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u0394 ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948.
\n\u092a\u094d\u0930\u092e\u093e\u0923:\u00a0<\/strong>\u0394 ABD \u0924\u0925\u093e \u0394 ACD \u092e\u0947\u0902,
\nDB = DC \u00a0 \u00a0[\u091a\u0942\u0901\u0915\u093f D BC \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 ]
\n\u2220 BDA\u00a0= \u2220CDA\u00a0[90\u0966\u00a0<\/sup>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915].
\nAD = AD [\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920’]
\nSAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 ABD\u00a0\u2245\u00a0\u0394 ACD
\nAB =AC [by CPCT]
\n\u0905\u0924:, \u0394 ABC\u00a0\u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3.\u00a0<\/strong>ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902\u00a0BE \u0914\u0930 CF \u092a\u0930 \u0915\u094d\u0930\u092e\u0936\u0903 \u0936\u0940\u0930\u094d\u0937\u0932\u092e\u094d\u092c AC \u0914\u0930 AB \u0916\u0940\u0902\u091a\u0947\u00a0\u0917\u090f \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u092f\u0947 \u0936\u0940\u0930\u094d\u0937\u0932\u092e\u094d\u092c\u00a0\u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902\u0964<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902\u00a0BE\u00a0\u22a5 AC \u0914\u0930 CF\u00a0\u22a5 AB \u091c\u0939\u093e\u0901 AB = AC \u0939\u0948 |
\n\"Triangles
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0BE = CF.
\n\u092a\u094d\u0930\u092e\u093e\u0923\u00a0:\u00a0<\/strong>\u00a0\u092f\u0939\u093e\u0901,\u00a0BE\u00a0\u22a5 AC \u0914\u0930 CF\u00a0\u22a5\u00a0AB\u00a0\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u0394ABE \u0914\u0930 \u0394 ACF \u092e\u0947\u0902
\n\u2220 AEB = \u2220 AFC \u00a0(90\u0966<\/sup>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915)
\n\u2220 A = \u2220 A (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nAB = AC (\u0926\u093f\u092f\u093e \u0939\u0948\u00a0)
\nASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0915\u0938\u094c\u091f\u0940 \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABE \u00a0\u2245\u00a0\u00a0\u0394 ACF
\n\u2234\u00a0BE = CF [ By CPCT ]
\nProved.<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AC \u0914\u0930 AB\u00a0\u092a\u0930 \u0916\u0940\u0902\u091a\u0947 \u0917\u090f \u0936\u0940\u0930\u094d\u0937\u0932\u0902\u092c\u00a0<\/strong>BE \u0914\u0930\u00a0CF<\/strong>\u00a0\u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902 \u00a0(\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f). \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0<\/strong>
\n(i) \u0394 ABE \u2245 \u0394 ACF<\/strong>
\n(ii) AB = AC, \u0905\u0930\u094d\u0925\u093e\u0924, \u0394ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948|<\/strong>
\n\"Triangles
\n\u0939\u0932 :\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902
\nBE\u00a0\u22a5 AC \u0914\u0930 CF\u00a0\u22a5 AB \u0939\u0948 \u0914\u0930 BE = CF \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n(i) \u0394 ABE \u2245 \u0394 ACF
\n(ii) AB = AC,\u0905\u0930\u094d\u0925\u093e\u0924,\u00a0\u0394ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>
\n(i) \u0394 ABE \u0924\u0925\u093e \u0394 ACF \u092e\u0947\u0902
\nBE = CF (\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220 AEB = \u2220 AFC (90\u0966<\/sup>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 )
\n\u2220 A = \u2220 A (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 \u0938\u0947
\n\u0394 ABE \u2245 \u0394 ACF [\u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 -I ]
\n(ii) AB = AC \u00a0[By CPCT]
\n\u0907\u0938\u0932\u093f\u090f, ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5.\u00a0ABC \u0914\u0930 DBC \u0938\u093e\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 BC \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0926\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f). \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u2220 ABD = \u2220 ACD \u0939\u0948|<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\"Class
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u0914\u0930 DBC \u0938\u093e\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 BC \u092a\u0930 \u092c\u0928\u0947 \u0926\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u2220 ABD = \u2220 ACD
\n\u092a\u094d\u0930\u092e\u093e\u0923:\u00a0<\/strong>ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |
\nAB = AC (\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2234 \u2220 ABC\u00a0= \u2220 ACB\u00a0 ………. (1)
\n(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,
\nBCD \u092d\u0940 \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |
\nBD = CD (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2234 \u2220 DBC\u00a0= \u2220 DCB ………. (2)
\n(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u2220 ABC\u00a0+\u00a0\u2220 DBC\u00a0= \u2220 ACB +\u00a0\u2220 DCB
\nOr, \u2220 ABD = \u2220 ACD
\nProved.<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6. \u0394ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902\u00a0AB = AC \u0939\u0948|\u00a0\u092d\u0941\u091c\u093e BA \u092c\u093f\u0902\u0926\u0941 D \u0924\u0915 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f AD = AB\u00a0<\/strong>\u0939\u0948\u00a0<\/strong>(\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f)| \u00a0\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u2220 BCD \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 |\u00a0<\/strong>
\n\"NCERT
\n\u0939\u0932 :\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>\u0394ABC \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948 |
\n\u092d\u0941\u091c\u093e BA \u0915\u094b \u092c\u093f\u0902\u0926\u0941 D \u0924\u0915 \u092c\u0922\u093e\u0908 \u0917\u092f\u0940 \u0939\u0948 \u091c\u093f\u0938\u0938\u0947 AD = AB \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u2220 BCD\u00a0<\/strong>= 90\u0966<\/sup>
\n\u092a\u094d\u0930\u092e\u093e\u0923:\u00a0<\/strong>
\nAB = AC ………….. (1) \u00a0(\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0914\u0930 \u00a0AB = AD ………….. (2) \u00a0(\u0926\u093f\u092f\u093e \u0939\u0948)
\n\"Class
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0938\u0947 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |
\nAC = AD ……………(3)
\n\u2234 \u22203 =\u00a0\u22204 …….. (4)\u00a0(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 ..)
\n\u0905\u092c,\u00a0AB = AC [\u0938\u092e\u0940\u0966 (1) \u0938\u0947]
\n\u2234 \u22201\u00a0=\u00a0\u22202 …. (5)\u00a0(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 ..)
\n\u0394ABC \u092e\u0947\u0902
\n\u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0923\u00a0\u22205 =\u00a0\u22201 +\u00a0\u22202 (\u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0923 \u0905\u0924:\u0905\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948 )
\n\u0905\u0925\u0935\u093e, \u22205 =\u00a0\u22202\u00a0+\u00a0\u22202 [ \u0938\u092e\u0940\u0966 (5) \u0938\u0947]
\n\u0905\u0925\u0935\u093er, \u22205 = 2\u22202\u00a0 ……. (6)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,
\n\u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0923\u00a0\u22206\u00a0=\u00a0\u22203\u00a0+\u00a0\u22204
\n\u0905\u0925\u0935\u093e, \u00a0\u22206\u00a0= 2\u22203 [\u0938\u092e\u0940\u0966 \u00a0(7) \u0938\u0947
\n\u0938\u092e\u0940\u0915\u0930\u0923 (6) \u0924\u0925\u093e (7) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930]
\n\u22205 +\u00a0\u22206 \u00a0= 2\u22202\u00a0+ 2\u22203
\n\u22205 +\u00a0\u22206 \u00a0= 2(\u22202\u00a0+ \u22203)
\n\u0905\u0925\u0935\u093e,\u00a0\u00a0180\u0966\u00a0<\/sup>=\u00a02(\u22202\u00a0+\u00a0\u22203) [\u00a0\u2235\u00a0\u2220BAC\u00a0+\u00a0\u2220DAC\u00a0\u00a0=\u00a0180\u0966\u00a0<\/sup>]
\n\u0905\u0925\u0935\u093e,\u00a0 \u2220BCD = 90\u0966
\n<\/sup>Proved.<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q7.\u00a0ABC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902\u00a0\u2220 A = 90\u00b0 \u0914\u0930 AB = AC. \u0924\u094b \u2220 B \u0914\u0930 \u2220 C \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |\u00a0<\/strong>
\n\u0939\u0932 \u00a0<\/strong>
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948\u00a0:<\/strong>\u00a0ABC\u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902
\n\u2220 A = 90\u00b0 \u0914\u0930 AB = AC \u0939\u0948 |
\n\u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u0939\u0948\u00a0<\/strong>:\u00a0\u2220B and\u00a0\u2220C
\nAB = AC (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2234 \u2220B\u00a0=\u00a0\u2220C …………(1)
\n(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092e\u0947\u0902,
\n\u2220A +\u00a0\u2220B +\u00a0\u2220C = 180\u0966\u00a0<\/sup>(\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917)
\n90\u00b0 +\u00a0\u2220B +\u00a0\u2220B =\u00a0180\u0966\u00a0<\/sup>\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947
\n2\u00a0\u2220B =\u00a0180\u0966\u00a0<\/sup>–\u00a090\u00b0
\n2\u00a0\u2220B =\u00a090\u00b0
\n\u2220B = \u00a045\u00b0
\n\u2234\u00a0\u2220B =\u00a045\u00b0 and\u00a0\u2220C =\u00a0\u00a045\u00b0<\/p>\n

Ex 7.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q8. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094b\u0923 60\u00b0 \u0915\u093e \u0939\u094b\u0924\u093e \u0939\u0948|<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\"Class
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>ABC \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902
\nAB = BC = AC
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n\u2220A =\u00a0\u2220B =\u00a0\u2220C =\u00a060\u00b0
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>
\nAB = AC (\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220B =\u00a0\u2220C ……… (1) \u00a0 [\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923]
\nAB = BC (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220A\u00a0=\u00a0\u2220C\u00a0 ………. (2) \u00a0 [\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923]
\nAC\u00a0= BC (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220A\u00a0=\u00a0\u2220B ………… (3) \u00a0 [\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923]
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1), (2) \u0914\u0930 (3) \u0938\u0947 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |
\n\u2220A\u00a0=\u00a0\u2220B\u00a0=\u00a0\u2220C\u00a0 ………….. (4)
\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092e\u0947\u0902
\n\u2220A\u00a0+\u00a0\u2220B\u00a0+\u00a0\u2220C = 180\u00b0
\n\u2220A\u00a0+\u00a0\u2220A\u00a0+\u00a0\u2220A = 180\u00b0
\n3\u00a0\u2220A = 180\u00b0
\n\u2220A = 60\u00b0
\n\u2234\u00a0\u2220A\u00a0=\u00a0\u2220B\u00a0=\u00a0\u2220C =\u00a060\u00b0<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.3<\/strong><\/span><\/p>\n

Ex 7.3 Class 9 \u0917\u0923\u093f\u0924 Q1. <\/strong>\u0394ABC \u0914\u0930\u00a0<\/strong>\u0394DBC \u090f\u0915 \u0939\u0940 \u0906\u0927\u093e\u0930 BC \u092a\u0930 \u092c\u0928\u0947 \u0926\u094b \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902 \u0915\u093f A \u0914\u0930 D \u092d\u0941\u091c\u093e BC \u0915\u0947 \u090f\u0915 \u0939\u0940 \u0913\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f)| \u092f\u0926\u093f AD \u092c\u095d\u093e\u0928\u0947 \u092a\u0930 BC \u0915\u094b P \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0947, \u0924\u094b \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n\"9th
\n(i)\u00a0\u00a0<\/strong>\u0394ABD\u00a0<\/strong>\u00a0\u2245\u00a0\u0394ACD<\/strong>
\n(ii) \u00a0<\/strong>\u0394ABP\u00a0<\/strong>\u00a0\u2245\u00a0\u0394ACP<\/strong>
\n(iii)\u00a0 AP \u0915\u094b\u0923 A \u0914\u0930 \u0915\u094b\u0923 D \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |<\/strong>
\n(iv) AP \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u093e \u0932\u092e\u094d\u092c \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948 |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u0394ABC \u0914\u0930\u00a0\u0394DBC \u0926\u094b \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902 \u0914\u0930 AD \u0915\u094b \u092c\u095d\u093e\u0928\u0947 \u092a\u0930 BC \u0915\u094b P \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\"CBSE
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i)\u00a0\u00a0\u0394ABD\u00a0\u2245\u00a0\u0394ACD
\n(ii) \u00a0\u0394ABP\u00a0\u2245\u00a0\u0394ACP
\n(iii)\u00a0 AP \u0915\u094b\u0923 A \u0914\u0930 \u0915\u094b\u0923 D \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n(iv) AP \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u093e \u0932\u092e\u094d\u092c \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0ABC \u0906\u0927\u093e\u0930 BC \u092a\u0930 \u092c\u0928\u093e \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f, AB = AC …….. (i)
\n\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, DBC \u092d\u0940 \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 |
\n\"NCERT
\n\"NCERT
\n\u0938\u092e\u0940\u0915\u0930\u0923 (iii) \u0914\u0930 (iv) \u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f AP \u0915\u094b\u0923 A \u0914\u0930 \u0915\u094b\u0923 D \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948|
\nProved (III).
\n\"NCERT
\n\u091a\u0942\u0901\u0915\u093f\u00a0\u2220DPB = 90\u00b0 \u0939\u0948\u0902 \u0914\u0930 BP = CP \u0938\u092e\u0940\u0966 (vi) \u0938\u0947 \u092f\u0939 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f AP \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u093e \u0932\u092e\u094d\u092c \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948|
\nProved (IV).<\/p>\n

Ex 7.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. AD \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u093e \u090f\u0915 \u0936\u0940\u0930\u094d\u0937\u0932\u092e\u094d\u092c \u0939\u0948<\/strong>, \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n\"NCERT
\n(i) AD \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/strong>
\n(ii) AD \u0915\u094b\u0923 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0AD \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u093e \u090f\u0915 \u0936\u0940\u0930\u094d\u0937\u0932\u092e\u094d\u092c \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948\u0964
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) AD \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964
\n(ii) AD \u0915\u094b\u0923 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>\u200b
\n\"NCERT
\n\u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0938\u0947 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f AD \u0930\u0947\u0916\u093e\u0916\u0902\u0921 BC \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964
\n\u0914\u0930 \u0938\u092e\u0940\u0915\u0930\u0923 (ii) \u0938\u0947 \u092f\u0939 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f AD \u0915\u094b\u0923 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n

Ex 7.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u0940 \u0926\u094b \u092d\u0941\u091c\u093e\u090f\u0901 AB \u0914\u0930 BC \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e AM \u0915\u094d\u0930\u092e\u0936\u0903 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 PQ \u0914\u0930 QR \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e PN \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f)\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n\"NCERT
\n\"Maths
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u0940 \u0926\u094b \u092d\u0941\u091c\u093e\u090f\u0901 AB \u0914\u0930 BC \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e AM \u0915\u094d\u0930\u092e\u0936\u0903 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 PQ \u0914\u0930 QR \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e PN \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902 |
\n\"Class
\n\"NCERT<\/p>\n

Ex 7.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0<\/strong>BE \u0914\u0930 CF \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u0947 \u0926\u094b \u092c\u0930\u093e\u092c\u0930 \u0936\u0940\u0930\u094d\u0937\u0932\u0902\u092c \u0939\u0948\u0902| RHS \u0938\u0930\u094d\u0935\u093e\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0394<\/strong>ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902 |<\/strong>
\n\u0939\u0932 :
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092e\u0947\u0902 \u0926\u094b \u092c\u0930\u093e\u092c\u0930 \u0936\u0940\u0930\u094d\u0937\u0932\u0902\u092c BE \u0914\u0930 CF \u0939\u0948\u0902 |
\n\u0905\u0924: BE = CF \u0939\u0948, BE\u00a0\u22a5\u00a0AC \u0914\u0930 CF\u00a0\u22a5\u00a0AB \u0939\u0948 |<\/p>\n

Q5. ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948 | AP\u00a0<\/strong>\u22a5\u00a0BC \u0916\u0940\u0902\u091a \u0915\u0930 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0<\/strong>\u2220B =\u00a0<\/strong>\u2220C \u0939\u0948 |\u00a0<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 AB = AC \u0939\u0948 | \u091c\u093f\u0938\u092e\u0947\u0902 AP\u00a0\u22a5\u00a0BC \u0939\u0948\u0902 |
\n\"NCERT<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.4<\/strong><\/span><\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924 Q1. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092e\u0947\u0902 \u0915\u0930\u094d\u0923 \u0938\u092c\u0938\u0947 \u0932\u0902\u092c\u0940 \u092d\u0941\u091c\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u093e
\n\u0915\u094b\u0923 B \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 \u0914\u0930 AC \u0915\u0930\u094d\u0923 \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n\"NCERT
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394 ABC \u0915\u093e \u2220B \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 |
\n\u0905\u0924: \u2220A \u0914\u0930 \u2220C \u0928\u094d\u092f\u0942\u0928\u0915\u094b\u0923 \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f, \u2220B > \u2220C\u00a0 [\u0915\u094d\u092f\u094b\u0902\u0915\u093f B \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 \u0914\u0930 C \u0928\u094d\u092f\u0942\u0928\u0915\u094b\u0923 \u0939\u0948 ]
\n\u2234 AC > AB\u00a0 (i) (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u092a\u0941\u0928: \u2220B \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 \u0914\u0930 \u2220A \u0928\u094d\u092f\u0942\u0928\u0915\u094b\u0923 \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f, \u2220B > \u2220A\u00a0 [\u0915\u094d\u092f\u094b\u0902\u0915\u093f B \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 \u0914\u0930 C \u0928\u094d\u092f\u0942\u0928\u0915\u094b\u0923 \u0939\u0948 ]
\n\u2234 AC > BC \u00a0(ii) (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0938\u092e\u0940\u0966 (i) \u0924\u0925\u093e (ii) \u0938\u0947 \u0915\u0930\u094d\u0923 AC \u0938\u092c\u0938\u0947 \u092c\u095c\u0940\u00a0 \u092d\u0941\u091c\u093e \u0939\u0948 |
\nProved.<\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u0906\u0915\u0943\u0924\u093f 7.48 \u092e\u0947\u0902,\u00a0<\/strong>\u0394<\/strong>ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 AB \u0914\u0930 AC \u0915\u094b \u0915\u094d\u0930\u092e\u0936: \u092c\u093f\u0928\u094d\u0926\u0941\u0913\u0902 P \u0924\u0925\u093e Q \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948| \u0938\u093e\u0925 \u0939\u0940,\u00a0<\/strong>\u2220<\/strong>PBC <\u00a0<\/strong>\u2220<\/strong>QCB \u0939\u0948| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f AC > AB \u0939\u0948|
\n\u0939\u0932 :<\/strong>
\n\"NCERT
\n<\/strong>\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0\u0394ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 AB \u0914\u0930 AC \u0915\u094b \u0915\u094d\u0930\u092e\u0936: \u092c\u093f\u0928\u094d\u0926\u0941\u0913\u0902 P \u0924\u0925\u093e Q \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902,\u00a0\u2220PBC < \u2220QCB \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0AC > AB
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0AB \u0914\u0930 AC \u0915\u094b \u0915\u094d\u0930\u092e\u0936: \u092c\u093f\u0928\u094d\u0926\u0941\u0913\u0902 P \u0924\u0925\u093e Q \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948,
\n\u0907\u0938\u0932\u093f\u090f, \u2220ABC + \u2220PBC = 180\u00b0 …… (1) \u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e
\n\u0914\u0930\u00a0\u00a0\u00a0 \u2220ACB + \u2220QCB = 180\u00b0 …… (2) \u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0938\u0947
\n\u2220ABC + \u2220PBC = \u2220ACB + \u2220QCB (\u091a\u0942\u0901\u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0938\u092e\u0940\u0966 \u0915\u093e \u092e\u093e\u0928 \u0938\u092e\u093e\u0928 \u0939\u0948)
\n\u091c\u092c\u0915\u093f \u2220PBC < \u2220QCB (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0905\u0924: \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f
\n\u2220ABC > \u2220ACB
\nProved.<\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u0906\u0915\u0943\u0924\u093f 7.49 \u092e\u0947\u0902,\u00a0<\/strong>\u2220<\/strong>B <\u00a0<\/strong>\u2220<\/strong>A \u0914\u0930\u00a0<\/strong>\u2220<\/strong>C <\u00a0<\/strong>\u2220<\/strong>D \u0939\u0948 |\u00a0<\/strong>\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f AD < BC \u0939\u0948 |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"Maths
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u0394 AOB \u0914\u0930 \u0394 COD \u092e\u0947\u0902 \u2220B < \u2220A \u0914\u0930 \u2220C < \u2220D \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0AD < BC
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394 AOB \u092e\u0947\u0902,
\n\u2220B < \u2220A\u00a0 (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2234\u00a0 AO < BO\u00a0 …. (1)\u00a0\u00a0 (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0905\u092c, \u0394 COD \u092e\u0947\u0902,
\n\u2220C < \u2220D\u00a0 (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2234\u00a0 DO < CO\u00a0 …. (2)\u00a0\u00a0 (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\nAO + DO < BO + CO
\n\u092f\u093e AD < BC
\nProved.<\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0<\/strong>AB \u0914\u0930 CD \u0915\u094d\u0930\u092e\u0936: \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u0915\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0914\u0930 \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u092d\u0941\u091c\u093e \u0939\u0948\u0902 (\u0926\u0947\u0916\u093f\u092f\u0947 \u0906\u0915\u0943\u0924\u093f)| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u00a0<\/strong>\u2220<\/strong>A >\u00a0<\/strong>\u2220<\/strong>C \u0914\u0930\u00a0<\/strong>\u2220<\/strong>B >\u00a0<\/strong>\u2220<\/strong>D \u0939\u0948|<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"Class
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0AB \u0914\u0930 CD \u0915\u094d\u0930\u092e\u0936: \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u0915\u0940
\n\u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0914\u0930 \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u092d\u0941\u091c\u093e \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) \u2220A > \u2220C
\n(ii) \u2220B > \u2220D
\n\u0930\u091a\u0928\u093e :\u00a0<\/strong>A \u0915\u094b C \u0938\u0947 \u0914\u0930 B \u0915\u094b D \u0938\u0947 \u092e\u093f\u0932\u093e\u092f\u093e|
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>(i)<\/strong>\u00a0\u0394ABC \u092e\u0947\u0902,
\n\"NCERT
\nAB \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u092d\u0941\u091c\u093e \u0939\u0948, (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0905\u0924:, BC > AB
\n\u2234 \u22202 > \u22205 …… (1) (\u092c\u095c\u0947 \u092d\u0941\u091c\u093e \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0905\u092c, \u0394ACD \u092e\u0947\u0902,
\nCD \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u092d\u0941\u091c\u093e \u0939\u0948, (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0905\u0924:, CD > AD
\n\u2234 \u22201 > \u22206 …… (2) (\u092c\u095c\u0947 \u092d\u0941\u091c\u093e \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0938\u092e\u0940\u0966 (1) \u0924\u0925\u093e (2) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u22201 + \u22202 > \u22205 + \u22206
\n\u092f\u093e\u00a0 \u2220A > \u2220C
\nProved.
\n(ii) \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0394ABD \u092e\u0947\u0902,
\nAD > AB (\u0915\u094d\u092f\u094b\u0902\u0915\u093f AB \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u092d\u0941\u091c\u093e \u0939\u0948)
\n\u2234 \u22203 > \u22208\u00a0 …… (3)
\n\u0914\u0930 \u0394BCD \u092e\u0947\u0902,
\nCD > BC (\u0915\u094d\u092f\u094b\u0902\u0915\u093f CD \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u092d\u0941\u091c\u093e \u0939\u0948)
\n\u2234 \u22204 > \u22207 …… (4)
\n\u0938\u092e\u0940\u0966 (3) \u0924\u0925\u093e (4) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u22203 + \u22204 > \u22207 + \u22208
\n\u092f\u093e \u2220B > \u2220D
\nProved.<\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u0906\u0915\u0943\u0924\u093f\u00a0<\/strong>\u092e\u0947\u0902\u00a0<\/strong>PR > PQ \u00a0\u0939\u0948 \u0914\u0930 PS \u0915\u094b\u0923 QPR \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 | \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u00a0<\/strong>\u2220<\/strong>PSR >\u00a0<\/strong>\u2220<\/strong>PSQ \u00a0\u0939\u0948 |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0PR > PQ \u0914\u0930 PS \u0915\u094b\u0923 QPR \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u2220PSR > \u2220PSQ\u00a0\u00a0<\/strong>
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0PS \u0915\u094b\u0923 QPR \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 | (\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2234 \u2220QPS = \u2220RPS \u2026\u2026 (1)
\n\u0914\u0930,\u00a0 PR > PQ \u00a0\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2234 <\/b>\u2220PQS > \u2220PRS .\u2026\u2026(2)
\n\u0394PQS \u092e\u0947\u0902,
\n\u2220QPS + \u2220PQS + \u2220PSQ = 180\u00b0 ….. (3) (\u0394 \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930, \u0394PRS \u092e\u0947\u0902,
\n\u2220PRS + \u2220RPS + \u2220PSR = 180\u00b0 …. (4) (\u0394 \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (3) \u0914\u0930 (4) \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948 \u0915\u093f ..
\n\u2220QPS + \u2220PQS + \u2220PSQ = \u2220PRS + \u2220RPS + \u2220PSR
\n\"NCERT
\n\u092f\u093e \u2220PQS + \u2220PSQ = \u2220PRS + \u2220PSR
\n\u091c\u092c\u0915\u093f \u2220PQS > \u2220PRS \u00a0\u00a0\u0938\u092e\u0940\u0966 (2) \u0938\u0947
\n\u0905\u0924: \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f \u2220PSQ < \u2220PSR
\nProved.<\/p>\n

Ex 7.4 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6.<\/strong>\u00a0\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u090f\u0915 \u0930\u0947\u0916\u093e \u092a\u0930 \u090f\u0915 \u0926\u093f\u090f \u0939\u0941\u090f \u092c\u093f\u0902\u0926\u0941 \u0938\u0947<\/strong>,\u00a0<\/strong>\u091c\u094b \u0909\u0938 \u0930\u0947\u0916\u093e \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948<\/strong>,\u00a0<\/strong>\u091c\u093f\u0924\u0928\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921\u00a0<\/strong>\u0916\u0940\u0902\u091a\u0947 \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0909\u0928\u092e\u0947\u0902 \u0932\u092e\u094d\u092c \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0m \u090f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 \u0914\u0930 O \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948
\n\u091c\u094b m \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948| OP\u00a0\u22a5\u00a0m
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0OP < OQ < OR < OS
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>OP\u00a0\u22a5\u00a0m\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u2234 \u2220OPQ = 90\u00b0 \u0914\u0930 \u2220OQP, \u2220ORP, \u2220OSP \u0928\u094d\u092f\u0942\u0928\u0915\u094b\u0923 \u0939\u0948\u0902 |
\n\u0905\u0924: \u2220OQP < \u2220OPQ
\n\u2234\u00a0\u00a0 OP < OQ ….. (1)\u00a0 (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930, \u2220ORP < \u2220OPQ
\n\u2234\u00a0\u00a0 OP < OR ….. (2) (\u092c\u095c\u0947 \u0915\u094b\u0923 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u095c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0938\u092e\u0940\u0966 (1) \u0924\u0925\u093e (2) \u0938\u0947
\nOP < OQ < OR
\nOP \u091c\u094b \u0932\u0902\u092c \u0939\u0948 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u092d\u0941\u091c\u093e \u0939\u0948|<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.5 (\u0910\u091a\u094d\u091b\u093f\u0915)<\/strong><\/span><\/p>\n

Ex 7.5 Class 9 \u0917\u0923\u093f\u0924 Q1. ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u092d\u094d\u092f\u0928\u094d\u0924\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u092c\u093f\u0928\u094d\u0926\u0941 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u094b \u2206ABC \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0936\u0940\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932-<\/strong>
\n\u090f\u0915 \u2206ABC \u0915\u0947 \u0905\u092d\u094d\u092f\u0928\u094d\u0924\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u092c\u093f\u0928\u094d\u0926\u0941 P \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u091c\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0936\u0940\u0930\u094d\u0937\u094b\u0902 A, B \u0935 C \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u094b\u0964
\n\u0930\u091a\u0928\u093e \u0935\u093f\u0927\u093f : \u0930\u091a\u0928\u093e \u0915\u0947 \u092a\u0926 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948\u0902-<\/p>\n

    \n
  1. \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u0926\u093f\u092f\u093e \u0939\u0941\u0906 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u092c\u0928\u093e\u0907\u090f\u0964<\/li>\n
  2. \u0905\u092c, AB \u0924\u0925\u093e BC \u0915\u0947 \u0932\u092e\u094d\u092c \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0916\u0940\u0902\u091a\u093f\u090f \u091c\u094b \u092a\u0930\u0938\u094d\u092a\u0930 \u092c\u093f\u0928\u094d\u0926\u0941 P \u092a\u0930 \u0915\u093e\u091f\u0947\u0902\u0964<\/li>\n
  3. \u0930\u0947\u0916\u093e\u0916\u0923\u094d\u0921 PA, PB \u0914\u0930 PC \u0916\u0940\u0902\u091a\u093f\u090f\u0964
    \n\u0905\u0924\u0903 P \u0905\u092d\u0940\u0937\u094d\u091f \u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948 \u091c\u094b \u0924\u0940\u0928\u094b\u0902 \u0936\u0940\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u0964<\/li>\n<\/ol>\n

    Ex 7.5 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u0915\u093f\u0938\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0905\u092d\u094d\u092f\u0928\u094d\u0924\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u092c\u093f\u0928\u094d\u0926\u0941 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0938\u092d\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u0964<\/strong>
    \n\"NCERT
    \n\u0939\u0932-<\/strong>
    \n\u092e\u093e\u0928\u093e ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0905\u092d\u094d\u092f\u0928\u094d\u0924\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u092c\u093f\u0928\u094d\u0926\u0941 P \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u091c\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC \u0914\u0930 CA \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u094b\u0964
    \n\u0930\u091a\u0928\u093e \u0935\u093f\u0927\u093f : \u0930\u091a\u0928\u093e \u0915\u0947 \u092a\u0926 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948\u0902-<\/p>\n

      \n
    1. \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u0926\u093f\u092f\u093e \u0939\u0941\u0906 \u2206ABC \u092c\u0928\u093e\u0907\u090f\u0964<\/li>\n
    2. \u2220B \u0914\u0930 \u2220C \u0915\u0947 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0916\u0940\u0902\u091a\u093f\u090f \u091c\u094b \u092a\u0930\u0938\u094d\u092a\u0930 \u092c\u093f\u0928\u094d\u0926\u0941 P \u092a\u0930 \u0915\u093e\u091f\u0947\u0902\u0964<\/li>\n
    3. \u0930\u0947\u0916\u093e\u0916\u0923\u094d\u0921 PB \u0924\u0925\u093e PC \u0916\u0940\u0902\u091a\u093f\u090f\u0964
      \n\u0905\u0924\u0903 P \u0905\u092d\u0940\u0937\u094d\u091f \u092c\u093f\u0928\u094d\u0926\u0941 \u0939\u0948 \u091c\u094b \u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u0964<\/li>\n<\/ol>\n

      Ex 7.5 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u090f\u0915 \u092c\u0921\u093c\u0947 \u092a\u093e\u0930\u094d\u0915 \u092e\u0947\u0902 \u0932\u094b\u0917 \u0924\u0940\u0928 \u092c\u093f\u0928\u094d\u0926\u0941\u0913\u0902 (\u0938\u094d\u0925\u093e\u0928\u094b\u0902) \u092a\u0930 \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u093f\u0924 \u0939\u0948\u0902<\/strong>
      \nA : \u091c\u0939\u093e\u0901 \u092c\u091a\u094d\u091a\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092b\u093f\u0938\u0932 \u092a\u091f\u094d\u091f\u0940 \u0914\u0930 \u091d\u0942\u0932\u0947 \u0939\u0948\u0902\u0964<\/strong>
      \nB : \u091c\u093f\u0938\u0915\u0947 \u092a\u093e\u0938 \u092e\u093e\u0928\u0935 \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u090f\u0915 \u091d\u0940\u0932 \u0939\u0948\u0964<\/strong>
      \nC : \u091c\u094b \u090f\u0915 \u092c\u0921\u093c\u0947 \u092a\u093e\u0930\u094d\u0915\u093f\u0902\u0917 \u0938\u094d\u0925\u0932 \u0914\u0930 \u092c\u093e\u0939\u0930 \u0928\u093f\u0915\u0932\u0928\u0947 \u0915\u0947 \u0930\u093e\u0938\u094d\u0924\u0947 \u0915\u0947 \u0928\u093f\u0915\u091f \u0939\u0948\u0964<\/strong>
      \n\u090f\u0915 \u0906\u0907\u0938\u0915\u094d\u0930\u0940\u092e \u0915\u093e \u0938\u094d\u091f\u0949\u0932 \u0915\u0939\u093e\u0901 \u0932\u0917\u093e\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0924\u093e\u0915\u093f \u0935\u0939\u093e\u0901 \u0932\u094b\u0917\u094b\u0902 \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0939\u0941\u0901\u091a \u0938\u0915\u0947?<\/strong>
      \n[\u0938\u0902\u0915\u0947\u0924 : \u0938\u094d\u091f\u0949\u0932 \u0915\u094b A, B \u0914\u0930 C \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964]<\/strong>
      \n\"NCERT
      \n\u0939\u0932-<\/strong>
      \nA, B \u0914\u0930 C \u0924\u0940\u0928 \u092c\u093f\u0928\u094d\u0926\u0941 \u0938\u094d\u0925\u093e\u0928 \u0939\u0948\u0902\u0964 \u0906\u0907\u0938\u0915\u094d\u0930\u0940\u092e \u0915\u093e \u0938\u094d\u091f\u0949\u0932 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0932\u094b\u0917\u094b\u0902 \u0915\u0940 \u0909\u0938 \u092a\u0930 \u0905\u0927\u093f\u0915\u0924\u092e \u092a\u0939\u0941\u0901\u091a \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0938\u094d\u091f\u0949\u0932 \u0924\u0940\u0928\u094b\u0902 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u094b\u0964
      \n\u0905\u0924: \u0906\u0907\u0938\u0915\u094d\u0930\u0940\u092e \u0938\u094d\u091f\u0949\u0932 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u0947 \u0938\u094d\u0925\u093e\u0928 (\u092c\u093f\u0928\u094d\u0926\u0941) P \u0915\u093e \u091a\u092f\u0928 \u0915\u0930\u0928\u093e \u0939\u0948 \u091c\u094b \u092a\u093e\u0930\u094d\u0915 \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u094b\u0964
      \n\u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0935\u093f\u0927\u093f\u0903<\/strong>
      \n1. \u092c\u093f\u0928\u094d\u0926\u0941 A \u0938\u0947 \u092c\u093f\u0928\u094d\u0926\u0941 B \u0915\u094b, \u092c\u093f\u0928\u094d\u0926\u0941 B \u0938\u0947 \u092c\u093f\u0928\u094d\u0926\u0941 C \u0915\u094b \u0914\u0930 \u092c\u093f\u0928\u094d\u0926\u0941 C \u0938\u0947 \u092c\u093f\u0928\u094d\u0926\u0941 A \u0915\u094b \u090b\u091c\u0941 \u0930\u0947\u0916\u093e\u0913\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092e\u093f\u0932\u093e\u0915\u0930 \u2206ABC \u092c\u0928\u093e\u0907\u090f\u0964
      \n2. \u0915\u093f\u0928\u094d\u0939\u0940\u0902 \u0926\u094b \u092d\u0941\u091c\u093e\u0913\u0902 (AB \u0935 BC) \u0915\u0947 \u0932\u092e\u094d\u092c \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0916\u0940\u0902\u091a\u093f\u090f \u091c\u094b \u092a\u0930\u0938\u094d\u092a\u0930 \u092c\u093f\u0928\u094d\u0926\u0941 P \u092a\u0930 \u0915\u093e\u091f\u0947\u0902\u0964
      \n\u0906\u0907\u0938\u0915\u094d\u0930\u0940\u092e \u0938\u094d\u091f\u0949\u0932 \u0915\u0947 \u091a\u092f\u0928 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0938\u094d\u0925\u093e\u0928 \u092c\u093f\u0928\u094d\u0926\u0941 P \u0939\u094b\u0917\u093e \u091c\u094b \u0924\u0940\u0928\u094b\u0902 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0938\u0947 \u0938\u092e\u0926\u0942\u0930\u0938\u094d\u0925 \u0939\u0948\u0964
      \n\"NCERT<\/p>\n

      Ex 7.5 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4. \u0938\u0902\u0932\u0917\u094d\u0928 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0937\u0921\u094d\u092d\u0941\u091c\u0940\u092f \u0914\u0930 \u0924\u093e\u0930\u0947 \u0915\u0947 \u0906\u0915\u093e\u0930 \u0915\u0940 \u0930\u0902\u0917\u094b\u0932\u093f\u092f\u094b\u0902 \u0915\u094b 1 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0938\u0947 \u092d\u0930\u0915\u0930 \u092a\u0942\u0930\u093e \u0915\u0940\u091c\u093f\u090f\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0917\u093f\u0928\u093f\u090f\u0964 \u0915\u093f\u0938\u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902?<\/strong>
      \n\"NCERT
      \n\u0939\u0932-<\/strong>
      \n\u091a\u093f\u0924\u094d\u0930\u094b\u0902 \u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f \u0935\u093f\u0915\u0930\u094d\u0923\u094b \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u092a\u0930 \u0937\u0921\u094d\u092d\u0941\u091c\u0940\u092f \u0906\u0915\u0943\u0924\u093f \u0915\u094b 6 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u0914\u0930 \u0924\u093e\u0930\u0947 \u0915\u0947 \u0906\u0915\u093e\u0930 \u0915\u0940 \u0906\u0915\u0943\u0924\u093f \u0915\u094b 12 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u092c\u0915\u093f \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092d\u0941\u091c\u093e 5 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964
      \n\"NCERT
      \n\u092a\u0941\u0928\u0903 \u0937\u0921\u094d\u092d\u0941\u091c\u0940\u092f \u0906\u0915\u0943\u0924\u093f \u0915\u0947 \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e 5 \u0938\u0947\u092e\u0940 \u0939\u0948, \u0915\u094b 1 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930 \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f 5 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u094b 1 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 25 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964
      \n\u0924\u092c \u0938\u094d\u0925\u093f\u0924\u093f 1 :<\/strong> \u0937\u0921\u094d\u092d\u0941\u091c\u0940\u092f \u0930\u0902\u0917\u094b\u0932\u0940 \u0907\u0938\u0915\u094b 1 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 6 x 25 = 150 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u092c\u093e\u0901\u091f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964
      \n\u0938\u094d\u0925\u093f\u0924\u093f 2 :<\/strong> \u0924\u093e\u0930\u0947 \u0915\u0947 \u0906\u0915\u093e\u0930 \u0915\u0940 \u0930\u0902\u0917\u094b\u0932\u0940
      \n5 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = 12
      \n\u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 1 \u0938\u0947\u092e\u0940 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = 12 x 25 = 300
      \n\u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f \u0924\u093e\u0930\u0947 \u0915\u0947 \u0906\u0915\u093e\u0930 \u0935\u093e\u0932\u0940 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/p>\n

      Hope given NCERT Solutions for Class 9 Maths Chapter 7 are helpful to complete your homework.<\/p>\n","protected":false},"excerpt":{"rendered":"

      NCERT Solutions for Class 9 Maths Chapter 7 Triangles (\u0924\u094d\u0930\u093f\u092d\u0941\u091c) (Hindi Medium) These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.1 Ex 7.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ACBD \u092e\u0947\u0902, AC = AD \u0939\u0948 \u0914\u0930 …<\/p>\n

      NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":7721,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[27,26,28,24,25],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (\u0924\u094d\u0930\u093f\u092d\u0941\u091c) (Hindi Medium) These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.1 Ex 7.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ACBD \u092e\u0947\u0902, AC = AD \u0939\u0948 \u0914\u0930 … NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/\" \/>\n<meta property=\"og:site_name\" content=\"NCERT Solutions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-23T05:39:09+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-07-23T09:40:28+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"720\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/ncertsolutions.guru\/#organization\",\"name\":\"NCERT Solutions\",\"url\":\"https:\/\/ncertsolutions.guru\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\",\"https:\/\/www.instagram.com\/ncertsolutionsguru\/\",\"https:\/\/www.linkedin.com\/in\/ncertsolutionsguru\/\",\"https:\/\/in.pinterest.com\/ncertsolutionsguru\/\",\"https:\/\/en.wikipedia.org\/wiki\/National_Council_of_Educational_Research_and_Training\",\"https:\/\/twitter.com\/ncertsolguru\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/ncertsolutions.guru\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1\",\"width\":460,\"height\":45,\"caption\":\"NCERT Solutions\"},\"image\":{\"@id\":\"https:\/\/ncertsolutions.guru\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/ncertsolutions.guru\/#website\",\"url\":\"https:\/\/ncertsolutions.guru\/\",\"name\":\"NCERT Solutions\",\"description\":\"NCERT Solutions for Class 1 to 12\",\"publisher\":{\"@id\":\"https:\/\/ncertsolutions.guru\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/ncertsolutions.guru\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"width\":1280,\"height\":720,\"caption\":\"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium)\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/#webpage\",\"url\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/\",\"name\":\"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) - 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Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 7.1 Ex 7.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ACBD \u092e\u0947\u0902, AC = AD \u0939\u0948 \u0914\u0930 … NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) Read More »","og_url":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/","og_site_name":"NCERT Solutions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2021-07-23T05:39:09+00:00","article_modified_time":"2021-07-23T09:40:28+00:00","og_image":[{"width":1280,"height":720,"url":"https:\/\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png","path":"\/home\/412375.cloudwaysapps.com\/bmvvpkvjjm\/public_html\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png","size":"full","id":7721,"alt":"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium)","pixels":921600,"type":"image\/png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/ncertsolutions.guru\/#organization","name":"NCERT Solutions","url":"https:\/\/ncertsolutions.guru\/","sameAs":["https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","https:\/\/www.instagram.com\/ncertsolutionsguru\/","https:\/\/www.linkedin.com\/in\/ncertsolutionsguru\/","https:\/\/in.pinterest.com\/ncertsolutionsguru\/","https:\/\/en.wikipedia.org\/wiki\/National_Council_of_Educational_Research_and_Training","https:\/\/twitter.com\/ncertsolguru"],"logo":{"@type":"ImageObject","@id":"https:\/\/ncertsolutions.guru\/#logo","inLanguage":"en-US","url":"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1","contentUrl":"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1","width":460,"height":45,"caption":"NCERT Solutions"},"image":{"@id":"https:\/\/ncertsolutions.guru\/#logo"}},{"@type":"WebSite","@id":"https:\/\/ncertsolutions.guru\/#website","url":"https:\/\/ncertsolutions.guru\/","name":"NCERT Solutions","description":"NCERT Solutions for Class 1 to 12","publisher":{"@id":"https:\/\/ncertsolutions.guru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ncertsolutions.guru\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png?fit=1280%2C720&ssl=1","contentUrl":"https:\/\/i0.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Hindi-Medium.png?fit=1280%2C720&ssl=1","width":1280,"height":720,"caption":"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium)"},{"@type":"WebPage","@id":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/#webpage","url":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-7-hindi\/","name":"NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Hindi Medium) - 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