{"id":2819,"date":"2021-07-23T10:20:21","date_gmt":"2021-07-23T04:50:21","guid":{"rendered":"http:\/\/ncertsolutions.guru\/?p=2819"},"modified":"2021-07-23T17:37:56","modified_gmt":"2021-07-23T12:07:56","slug":"ncert-solutions-for-class-9-maths-chapter-6-hindi","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-6-hindi\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Hindi Medium)"},"content":{"rendered":"

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (\u0930\u0947\u0916\u093e\u090f\u0901 \u0914\u0930 \u0915\u094b\u0923) (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 6 Lines and Angles.<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.1<\/strong><\/span><\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u00a0\u0906\u0915\u0943\u0924\u093f. 6.13 \u092e\u0947\u0902, \u0930\u0947\u0916\u093e\u090f\u0901 AB \u0914\u0930 CD \u092c\u093f\u0902\u0926\u0941 O \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 | \u092f\u0926\u093f \u00a0\u2220AOC + \u2220 BOE = 70\u00b0 \u0939\u0948 \u0914\u0930 \u2220BOD = 40\u00b0 \u0939\u0948 \u0924\u094b \u2220BOE \u0914\u0930 \u092a\u094d\u0930\u0924\u093f\u0935\u0930\u094d\u0924\u0940 \u2220COE \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |\u00a0<\/strong>
\n\u0939\u0932:<\/strong>
\n\"NCERT
\n\u2220BOD = 40\u00b0
\n\u2220AOC\u00a0 = \u2220BOD (\u0936\u0940\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u2220AOC = 40\u00b0
\n\u2220AOC\u00a0 + \u2220 BOE = 70\u00b0 (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220BOE = 70\u00b0
\n\u2220BOE = 70\u00b0 – 40\u00b0
\n\u2220BOE = 30\u00b0
\n\u091a\u0942\u0901\u0915\u093f, AOB \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f, \u2220AOC + \u00a0\u2220COE +\u2220BOE = 180\u00b0 (\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u21d2 70\u00b0 + \u2220COE = 180\u00b0
\n\u21d2\u00a0\u2220COE = 180\u00b0 – 70\u00b0
\n\u21d2\u00a0\u2220COE = 110\u00b0
\n\u092a\u094d\u0930\u0924\u093f\u0935\u0930\u094d\u0924\u0940 \u2220COE = 360 – 110\u00b0 = 250\u00b0<\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u0906\u0915\u0943\u0924\u093f 6.14 \u092e\u0947\u0902, \u0930\u0947\u0916\u093e\u090f\u0901 \u00a0XY \u0914\u0930 MN \u092c\u093f\u0902\u0926\u0941 O \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 | \u092f\u0926\u093f\u00a0\u2220POY = 90\u00b0 \u0914\u0930\u00a0a :\u00a0b= 2 : 3 \u0939\u0948 \u0924\u094b\u00a0\u00a0c \u00a0<\/em>\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u00a0|\u00a0<\/em><\/strong>
\n\u0939\u0932 :<\/strong>
\n\"Maths
\n\u2220POY=90\u00b0 (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u092e\u093e\u0928\u093e \u00a0\u2220a \u0914\u0930 \u2220b = 2x \u0914\u0930 3x \u0939\u0948 |
\n\u091a\u0942\u0901\u0915\u093f, XOY \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220a +\u00a0\u2220b +\u00a0\u2220POY = 180\u00b0 (\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u21d2 2x + 3x + 90\u00b0= 180\u00b0
\n\u21d2 5x\u00a0 = 180\u00b0 \u00ad\u00ad- 90\u00b0
\n\u21d2 5x = 90\u00b0
\n\u21d2 x = 18\u00b0
\n\u0905\u092c, \u2220a = 2 x 18\u00b0 = 36\u00b0
\n\u2220b =3 x 18\u00b0 = 54\u00b0
\n\u092f\u0939\u093e\u0901, MON \u092d\u0940 \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u2220b +\u00a0\u2220c = 180\u00b0(\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u222054\u00b0 +\u00a0\u2220c = 180\u00b0
\n\u21d2 \u2220c = 180\u00b0 – 54\u00b0 = 126\u00b0<\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u0906\u0915\u0943\u0924\u093f 6.15 \u092e\u0947\u0902,\u00a0\u2220PQR =\u00a0\u2220PRQ \u0939\u0948, \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u2220PQS =\u00a0\u2220PRT \u0939\u0948 |\u00a0<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u2220PQR =\u00a0\u2220PRQ
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>\u2220PQS =\u00a0\u2220PRT
\n\u092a\u094d\u0930\u092e\u093e\u0923\u00a0<\/strong>:
\n\u2220PQS +\u00a0\u2220PQR = 180\u00b0 \u00a0………. (1) \u00a0\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e
\n\u2220PRT +\u00a0\u2220PRQ\u00a0= 180\u00b0\u00a0 ………. (2) \u00a0\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\u2220PQS +\u00a0\u2220PQR =\u00a0\u2220PRT +\u00a0\u2220PRQ
\nOr, \u00a0\u2220PQS +\u00a0\u2220PQR =\u00a0\u2220PRT +\u00a0\u2220PQR \u00a0 \u00a0(\u2220PQR =\u00a0\u2220PRQ \u0926\u093f\u092f\u093e \u0939\u0948)
\n\"Class
\nOr,\u00a0\u2220PQS =\u00a0\u2220PRT \u0938\u093f\u0926\u094d\u0927 \u0939\u0941\u0906 |<\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4. \u0906\u0915\u0943\u0924\u093f 6.16 \u092e\u0947\u0902, \u092f\u0926\u093f x + y = w + y \u0939\u0948, \u0924\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f AOB \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948|\u00a0<\/strong>
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0x + y = w + z
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>AOB \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0x\u00a0+ y +\u00a0w + z\u00a0= 360\u0966<\/sup>
\n\u0905\u0925\u0935\u093e \u00a0\u00a0x\u00a0+ y + x + y = 360\u0966<\/sup>
\n\u21d2\u00a0 2x + 2y =\u00a0360\u0966<\/sup>
\n\u21d2 2 (x + y) =\u00a0360\u0966<\/sup>
\n\u21d2 x +\u00a0y\u00a0= 180\u0966 \u00a0<\/sup>\u00a0(\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u091c\u092c \u0915\u094b\u0908 \u0938\u0902\u0932\u0917\u094d\u0928 \u0926\u094b \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u00a0180\u0966\u00a0<\/sup>\u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u0930\u0947\u0916\u093e \u0938\u0940\u0927\u0940 \u090f\u0935\u0902 \u0938\u0930\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948 |
\n\u0905\u0924: AOB\u00a0\u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948|
\nHence Proved.<\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u0906\u0915\u0943\u0924\u093f 6.17 \u092e\u0947\u0902, POQ \u090f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 | \u0915\u093f\u0930\u0923 OR \u0930\u0947\u0916\u093e PQ \u092a\u0930 \u0932\u092e\u094d\u092c \u0939\u0948 | \u0915\u093f\u0930\u0923\u094b\u0902 OP \u0914\u0930 OR \u0915\u0947 \u092c\u0940\u091a \u092e\u0947\u0902 OS \u090f\u0915 \u0905\u0928\u094d\u092f \u0915\u093f\u0930\u0923 \u0939\u0948 | \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f:
\n\"NCERT
\n\"NCERT
\n\u0939\u0932:\u00a0<\/strong>
\n<\/strong>\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0\u200bPOQ \u090f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 \u0914\u0930 OR \u22a5\u00a0PQ \u0924\u0925\u093e OS\u00a0\u2220POR \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u0915\u093f\u0930\u0923 \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0
\n\"NCERT
\n<\/strong>\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0\u2220ROQ = 90\u0966<\/sup>\u00a0 \u00a0 ( \u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u0905\u092c, \u00a0\u2220POR +\u00a0\u2220ROQ\u00a0= 180\u0966\u00a0<\/sup>[\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e]
\n\u092f\u093e\u00a0 \u2220POR +\u00a090\u0966<\/sup>\u00a0= 180\u0966<\/sup>
\n\u092f\u093e\u00a0 \u2220POR = 180\u0966<\/sup>\u00a0–\u00a090\u0966<\/sup>
\n<\/sup><\/strong>\u092f\u093e \u00a0 \u00a0\u00a0\u2220POR\u00a0= 90\u0966
\n<\/sup>\u2220ROS =\u00a0\u2220POR –\u00a0\u2220POS\u00a0 ………. (1)
\n\u0914\u0930
\n\u2220ROS =\u00a0\u2220QOS\u00a0–\u00a0\u2220ROQ\u00a0 ……… (2)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u2220ROS +\u00a0\u2220ROS\u00a0=\u00a0\u2220QOS\u00a0–\u00a0\u2220ROQ +\u00a0\u2220POR –\u00a0\u2220POS
\n\u0905\u0925\u0935\u093e \u00a0 \u00a02\u2220ROS =\u00a0\u2220QOS\u00a0–\u00a090\u0966<\/sup>\u00a0+\u00a090\u0966<\/sup>\u00a0–\u00a0\u2220POS
\n\u0905\u0925\u0935\u093e \u00a0 \u00a02\u2220ROS\u00a0=\u00a0\u2220QOS –\u00a0\u2220POS
\n\"Maths
\nProved.<\/p>\n

Ex 6.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6. \u092f\u0939 \u0926\u093f\u092f\u093e \u0939\u0948 \u0915\u093f\u00a0\u2220 XYZ = 64\u00b0 \u0939\u0948 \u0914\u0930 XY \u0915\u094b \u092c\u093f\u0902\u0926\u0941 P \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 | \u0926\u0940 \u0939\u0941\u0908 \u0938\u0941\u091a\u0928\u093e \u0938\u0947 \u090f\u0915 \u0906\u0915\u0943\u0924\u093f \u0916\u0940\u0902\u091a\u093f\u090f | \u092f\u0926\u093f \u0915\u093f\u0930\u0923\u00a0YQ, \u2220 ZYP \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0924\u094b \u2220 XYQ \u0914\u0930 \u092a\u094d\u0930\u0924\u093f\u0935\u0930\u094d\u0924\u0940\u00a0\u00a0\u2220 QYP \u0915\u0947 \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |\u00a0<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\"Maths
\n\u2220 XYZ = 64\u00b0
\nYQ, \u2220 ZYP\u00a0\u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948;
\n\u0907\u0938\u0932\u093f\u090f
\n\u2220 QYP\u00a0= \u00a0\u2220 ZYQ \u00a0 \u00a0 ………… (1)
\nXY \u0915\u094b \u092c\u093f\u0902\u0926\u0941 P \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 |
\n\u2234 XYP \u090f\u0915 \u0938\u0930\u0932 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u0905\u0924:\u00a0\u2220 XYZ\u00a0+\u00a0\u2220 QYP +\u00a0\u2220 ZYQ = 180\u00b0 (\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u21d2 64\u00b0\u00a0+\u00a0\u2220 QYP +\u00a0\u2220 QYP\u00a0= 180\u00b0
\n\u21d2 2\u2220 QYP\u00a0= 180\u00b0 –\u00a064\u00b0
\n\u21d2 2\u2220 QYP\u00a0= 116\u00b0
\n\u21d2 \u2220 QYP\u00a0= 58\u00b0
\n\u21d2 \u2220 QYP\u00a0= \u00a0\u2220 ZYQ =\u00a058\u00b0
\n\u21d2 \u2220 XYQ =\u00a0\u2220XYZ +\u00a0\u2220 ZYQ = \u00a064\u00b0\u00a0+\u00a058\u00b0 = \u00a0122\u00b0
\n\u092a\u094d\u0930\u0924\u093f\u0935\u0930\u094d\u0924\u0940\u00a0\u2220 QYP\u00a0= 360\u00b0\u00a0– 58\u00b0 = 302\u00b0<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.2<\/strong><\/span><\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924 Q1. \u0906\u0915\u0943\u0924\u093f 6.28 \u092e\u0947\u0902, x \u0914\u0930 y \u0915\u0947 \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0914\u0930 \u092b\u093f\u0930 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f AB || CD \u0939\u0948\u0964<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>
\n\"Maths
\nx + 50\u00b0 = \u00a0180\u00b0 \u00a0 (\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u21d2 x =\u00a0180\u00b0\u00a0–\u00a0\u00a050\u00b0
\n\u21d2 x =\u00a0130\u00b0
\ny =\u00a0130\u00b0
\nx = y =\u00a0130\u00b0 (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u0938\u0947 )
\nAB || CD<\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924 Q2. \u0906\u0915\u0943\u0924\u093f 6.29 \u092e\u0947\u0902, \u092f\u0926\u093f AB || CD, CD || EF \u0914\u0930 y : z = 3 : 7 \u0939\u0948, \u0924\u094b x \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |\u00a0<\/strong>
\n\"Lines
\n\u0939\u0932 :<\/strong>
\nAB || CD …….. (1) \u0926\u093f\u092f\u093e \u0939\u0948 ;
\nCD || EF …….. (2) \u0926\u093f\u092f\u093e \u0939\u0948 ;
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948 \u0915\u093f
\nAB ||\u00a0EF ……….(3)
\n\u2234 x = z …….. (4) \u00a0 \u00a0 \u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923
\n\u0905\u092c, y = 3k\u00a0\u0924\u0925\u093e z = 7k\u00a0\u092e\u093e\u0928\u093e
\nAB || CD \u00a0\u0926\u093f\u092f\u093e \u0939\u0948;
\n\u2234 x + y =\u00a0180\u00b0 \u00a0 \u00a0(\u090f\u0915 \u0939\u0940 \u0913\u0930 \u0915\u0947 \u0905\u0902\u0924: \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 )
\n\u0905\u0925\u0935\u093e \u00a0 z\u00a0+ y =\u00a0180\u00b0
\n\u21d2 7k + 3k =\u00a0180\u00b0
\n\u21d2 10k =\u00a0\u00a0180\u00b0
\n\u21d2 k =\u00a0\u00a018\u00b0
\n\u091a\u0942\u0901\u0915\u093f \u00a0x = z \u0938\u092e\u0940\u0966 (4) \u0938\u0947
\n\u2234 x = 7k = 7\u00a0\u00d7 18\u00b0\u00a0= 126\u00b0<\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u0906\u0915\u0943\u0924\u093f 6.30 \u092e\u0947\u0902, \u092f\u0926\u093f\u00a0AB || CD, EF \u22a5 CD \u0914\u0930\u00a0\u2220 GED = 126\u00b0 \u0939\u0948,\u0924\u094b\u00a0\u2220 AGE, \u2220GEF\u00a0 \u00a0\u0914\u0930\u00a0\u2220 FGE \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\"NCERT
\n\u0939\u0932 :\u00a0<\/strong>\u2220GED = 126\u00b0
\nAB || CD \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u2234\u00a0\u2220AGE = \u2220GED (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923)
\n\u0905\u0924 :\u00a0\u2220AGE =\u00a0126\u00b0
\n\u2220GED = 126\u00b0
\n\u2220GED =\u00a0\u2220GEF +\u00a0\u2220FED\u00a0= 126\u00b0
\n\u2220GEF +\u00a0\u2220FED\u00a0= 126\u00b0
\n\u2220GEF +\u00a090\u00b0\u00a0= 126\u00b0 \u00a0 \u00a0(\u2235 EF\u00a0\u22a5\u00a0<\/strong>CD\u00a0\u2234\u00a0\u2220FED =\u00a090\u00b0)
\n\u2220GEF = 126\u00b0 –\u00a090\u00b0
\n\u2220GEF = 36\u00b0
\n\u0905\u092c,
\n\u2220AGE +\u00a0\u2220FGE =\u00a0180\u00b0 \u00a0 \u00a0( \u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e )
\n126\u00b0 +\u00a0\u2220FGE =\u00a0180\u00b0
\n\u2220FGE =\u00a0180\u00b0 –\u00a0126\u00b0
\n\u2220FGE\u00a0= 54\u00b0
\n\u2220AGE =\u00a0126\u00b0,\u00a0\u2220GEF = 36\u00b0 \u0914\u0930\u00a0\u2220FGE\u00a0=\u00a054\u00b0<\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u0906\u0915\u0943\u0924\u093f 6.31 \u092e\u0947\u0902, \u092f\u0926\u093fPQ || ST, \u2220 PQR = 110\u00b0 \u0914\u0930\u00a0\u2220 RST = 130\u00b0 \u0939\u0948, \u0924\u094b\u00a0\u2220QRS\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\"NCERT
\n[\u0938\u0902\u0915\u0947\u0924 : \u092c\u093f\u0902\u0926\u0941 R \u0938\u0947 \u0939\u094b\u0915\u0930 ST \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u090f\u0915 \u0930\u0947\u0916\u093e \u00a0\u0916\u093f\u091a\u093f\u090f|]<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u0930\u091a\u0928\u093e :\u00a0<\/strong>\u092c\u093f\u0902\u0926\u0941 R \u0938\u0947 \u00a0\u0939\u094b\u0915\u0930\u00a0XY ||\u00a0ST \u0916\u093f\u0902\u091a\u093e |
\nPQ || ST \u00a0 \u00a0………….. \u00a0(1) \u00a0\u0926\u093f\u092f\u093e \u0939\u0948 |
\n\"Lines
\nXY ||\u00a0ST \u00a0 \u00a0……………..(2) \u0930\u091a\u0928\u093e \u0938\u0947
\n\u0938\u092e\u0940\u0966 (1) \u0924\u0925\u093e (2) \u0938\u0947
\nPQ ||\u00a0XY \u00a0 …………….. (3)
\nXY ||\u00a0ST \u00a0\u00a0\u0930\u091a\u0928\u093e \u0938\u0947
\n\u2220RST +\u00a0\u2220SRY = 180\u00b0 \u00a0(\u090f\u0915 \u0939\u0940 \u0913\u0930 \u0915\u0947 \u0905\u0902\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u00a0)
\n\u21d2\u00a0\u00a0130\u00b0\u00a0+\u00a0\u2220SRY = 180\u00b0
\n\u21d2\u00a0\u00a0\u2220SRY = 180\u00b0 –\u00a0130\u00b0
\n\u21d2\u00a0\u00a0\u2220SRY = 50\u00b0
\nPQ ||\u00a0XY \u00a0 …………….. (3)\u00a0\u0938\u0947
\n\u2234 \u2220PQR =\u00a0\u2220QRY \u00a0 \u00a0(\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923)
\n110\u00b0 = \u00a0\u2220QRS +\u00a0\u2220SRY
\n110\u00b0 =\u00a0\u00a0\u2220QRS +\u00a050\u00b0
\n\u2220QRS\u00a0=\u00a0110\u00b0 –\u00a050\u00b0
\n\u2220QRS\u00a0= 60\u00b0<\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5 \u00a0\u0906\u0915\u0943\u0924\u093f6.32 \u092e\u0947\u0902, \u092f\u0926\u093f \u00a0AB || CD, \u2220 APQ = 50\u00b0 \u0914\u0930\u00a0\u2220 PRD = 127\u00b0 \u0939\u0948 ,\u0924\u094b x \u0914\u0930 Y\u00a0\u091c\u094d\u091e\u093e\u0924 \u00a0\u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\"Class
\n\u0939\u0932:<\/strong>\u00a0\u2220 APQ = 50\u00b0 \u0914\u0930\u00a0\u2220 PRD = 127\u00b0
\nAB || CD \u00a0 \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u2234 \u00a0\u2220APQ =\u00a0\u2220PQR \u00a0 \u00a0 \u00a0( \u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923 )
\n\u092f\u093e\u00a0 x = 50\u00b0
\n\u092a\u0941\u0928: \u2220APR \u00a0=\u00a0\u2220PRD\u00a0\u00a0 \u00a0 ( \u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923 )
\n\u092f\u093e y + 50\u00b0 =\u00a0127\u00b0
\n\u092f\u093e y =\u00a0127\u00b0 –\u00a050\u00b0
\n\u092f\u093e y = 77\u00b0
\nx = 50\u00b0 \u0914\u0930\u00a0y = 77\u00b0<\/p>\n

Ex 6.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6.\u0906\u0915\u0943\u0924\u093f 6.33 \u00a0\u092e\u0947\u0902 ,PQ \u0914\u0930 RS \u0926\u094b \u0939\u0948 \u091c\u094b \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u0924\u0930 \u0930\u0916\u0947 \u0917\u090f \u0939\u0948 | \u092f\u093e \u0906\u092a\u0924\u0928\u00a0\u0915\u093f\u0930\u0923 (incident ray )AB,\u0926\u0930\u094d\u092a\u0923 PQ \u0938\u0947 B \u092a\u0930 \u091f\u0915\u0930\u093e\u0924\u0940 \u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u0935\u093e\u0930\u094d\u0924\u093f\u0924 \u0915\u093f\u0930\u0923\u00a0(reflected ray ) \u092a\u0925 BC \u092a\u0930 \u091f\u0915\u0930\u093e\u0924\u0940 \u0939\u0948 \u0924\u0925\u093e \u092a\u0941\u0928\u0903 CD\u0915\u0947 \u0905\u0928\u0941\u0926\u093f\u0936 \u092a\u094d\u0930\u0935\u093e\u0930\u094d\u0924\u093f\u0924 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948 |\u00a0\u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f\u00a0\u00a0AB || CD \u0939\u0948 |<\/strong>
\n\"NCERT
\n\u0939\u0932:\u00a0<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948:<\/strong>\u00a0PQ || RS \u0914\u0930 AB \u090f\u0915 \u0906\u092a\u0924\u0928 \u0915\u094b\u0923 \u0939\u0948, CD \u090f\u0915 \u092a\u0930\u093e\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u093f\u0930\u0923 \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948\u00a0:<\/strong>\u00a0AB || CD
\n\u0930\u091a\u0928\u093e :<\/strong>
\nBM\u00a0\u22a5 PQ \u0914\u0930 CN\u00a0\u22a5 RS \u0916\u093f\u0902\u091a\u093e |
\n\"Class
\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong>
\nBM\u00a0\u22a5 PQ and CN\u00a0\u22a5 RS
\n\u2234 BM ||\u00a0CM \u0914\u0930 BC \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u2234\u00a0\u200b\u22202 =\u00a0\u2220 3 \u00a0 ………… (1) (\u090f\u0915\u093e\u0902\u0924\u0930 \u0905\u0902\u0924:\u0915\u094b\u0923 )
\n\u091c\u092c\u0915\u093f \u0939\u092e \u091c\u093e\u0928\u0924\u0947 \u0939\u0948 \u0915\u093f –
\n\u0906\u092a\u0924\u0928 \u0915\u094b\u0923 = \u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0928 \u0915\u094b\u0923, \u091c\u0939\u093e\u0901 BM \u0914\u0930 CN \u0905\u092d\u093f\u0932\u0902\u092c \u0939\u0948\u0902 |
\n\u2234\u00a0\u200b\u22201\u00a0=\u00a0\u2220 2 \u00a0 ………….. (2)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,
\n\u2234\u00a0\u200b\u22203\u00a0=\u00a0\u2220 4\u00a0 \u00a0………….. (3)
\n\u0938\u092e\u0940\u0966 (1), (2) \u0914\u0930 (3) \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948 |
\n\u22201\u00a0=\u00a0\u2220 4\u00a0 ……………. (4)
\n\u0938\u092e\u0940\u0966 (1) \u0924\u0925\u093e (4) \u0915\u094b \u091c\u094b\u095c\u0928\u0947 \u092a\u0930
\n\u22201\u00a0+\u00a0\u22202\u00a0=\u00a0\u2220 3\u00a0+\u00a0\u2220 4
\n\u2220ABC\u00a0=\u00a0\u2220 BCD\u00a0\u00a0(\u090f\u0915\u093e\u0902\u0924\u0930 \u0905\u0924: \u0915\u094b\u0923)
\n\u0907\u0938\u0932\u093f\u090f, AB || CD
\nProved.<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.3<\/strong><\/span><\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924 Q1. \u0906\u0915\u0943\u0924\u093f 6.39 \u092e\u0947\u0902, \u0394 PQR \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 QP \u0914\u0930 RQ \u0915\u094b \u0915\u094d\u0930\u092e\u0936: \u092c\u093f\u0928\u094d\u0926\u0941\u0913\u0902 S \u0914\u0930 T \u0924\u0915 \u092c\u0922\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 | \u092f\u0926\u093f \u2220SPR = 135\u00b0 \u0939\u0948 \u0914\u0930 \u2220 PQT = 110\u00b0 \u0939\u0948, \u0924\u094b \u2220 PRQ \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u2220QPR +\u00a0\u2220SPR = 180\u00b0 ( \u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e )
\n\u21d2 \u2220QPR +\u00a0135\u00b0\u00a0= 180\u00b0
\n\u21d2 \u2220QPR\u00a0\u00a0= 180\u00b0 –\u00a0135\u00b0
\n\u21d2 \u2220QPR\u00a0\u00a0= 45\u00b0
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,
\n\u2220PQR +\u00a0\u2220TQP\u00a0= 180\u00b0 ( \u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e )
\n\u21d2 \u2220PQR\u00a0+\u00a0110\u00b0\u00a0= 180\u00b0
\n\u21d2 \u2220PQR\u00a0\u00a0= 180\u00b0 –\u00a0110\u00b0
\n\u21d2 \u2220PQR\u00a0\u00a0= 70\u00b0
\n\u0905\u092c \u0924\u094d\u0930\u093f\u092d\u0941\u091c PQR \u092e\u0947\u0902,
\n\u2220QPR +\u00a0\u2220PQR +\u00a0\u2220PRQ =\u00a0180\u00b0
\n45\u00b0 + 70\u00b0 +\u00a0\u2220PRQ =\u00a0180\u00b0
\n115\u00b0 +\u00a0\u2220PRQ =\u00a0180\u00b0
\n\u2220PRQ =\u00a0180\u00b0 –\u00a0115\u00b0
\n\u2220PRQ = 65\u00b0<\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u2220X = 62\u00b0 \u0914\u0930 \u2220XYZ = 54\u00b0 \u0939\u0948\u0964 \u092f\u0926\u093f YO \u0914\u0930 \u2220O \u0915\u094d\u0930\u092e\u0936\u0903 \u2206XYZ \u0915\u0947 \u2220XYZ \u0914\u0930 \u2220XZY \u0915\u0947 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948\u0902, \u0924\u094b \u2220OZY \u0914\u0930 \u2220YOZ \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n\"Class
\n\u0939\u0932-<\/strong>
\n\u2206XYZ \u092e\u0947\u0902,
\n\u2220X + \u2220XYZ + \u2220XZY = 180\u00b0 (\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0905\u0928\u094d\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948\u0964)
\n62\u00b0 + 54\u00b0 + \u2220XZY = 180\u00b0
\n\u2220XZY = 180\u00b0 – (62\u00b0 + 54\u00b0) = 180\u00b0 – 116\u00b0 = 64\u00b0
\nYO, \u2220XYZ \u0915\u093e \u0914\u0930 \u2220O, \u2220XZY \u0915\u093e \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948\u0964
\n\u2220OYZ = \\(\\frac { 1 }{ 2 }\\) \u2220XY\u2220 \u0914\u0930 \u2220OZY = \\(\\frac { 1 }{ 2 }\\) XZY
\n\u2220OYZ = \\(\\frac { 1 }{ 2 }\\) x 54\u00b0 \u0914\u0930 \u2220OZY = \\(\\frac { 1 }{ 2 }\\) x 64\u0966
\n\u2220OYZ = 27\u00b0 \u0914\u0930 \u2220OZY = 32\u00b0
\n\u0924\u092c \u2206OYZ \u092e\u0947\u0902,
\n\u2220OYZ + \u2220OZY + \u2220YOZ = 180\u00b0 (\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u092d\u0940 \u0905\u0928\u094d\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948\u0964)
\n27\u00b0 + 32\u00b0 + \u2220YOZ = 180\u00b0
\n\u2220YOZ = 180\u00b0 – (27\u00b0 + 32\u00b0) = 180\u00b0 – 59\u00b0
\n\u2220YOZ = 121\u00b0
\n\u2220OZY = 32\u00b0 \u0924\u0925\u093e \u2220YOZ = 121\u00b0<\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u092f\u0926\u093f AB || DE, \u2220BAC = 35\u00b0 \u0914\u0930 \u2220CDE = 53\u00b0 \u0939\u0948, \u0924\u094b \u2220DCE \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n\"9th
\n\u0939\u0932-<\/strong>
\nAB || DE \u0914\u0930 \u090b\u091c\u0941 \u0930\u0947\u0916\u093e AE \u0907\u0928\u094d\u0939\u0947\u0902 \u0915\u093e\u091f\u0924\u0940 \u0939\u0948\u0964 \u0924\u092c,
\n\u2220BAE = \u2220AED (\u090f\u0915\u093e\u0928\u094d\u0924\u0930 \u0915\u094b\u0923)
\n\u092a\u0930\u0928\u094d\u0924\u0941 \u2220BAE = \u2220BAC \u0914\u0930 \u2220AED = \u2220CED
\n\u2220BAC = \u2220CED \u092f\u093e 35\u00b0 = \u2220CED
\n\u2220CED = 35\u00b0
\n\u0924\u092c \u0394CDE \u092e\u0947\u0902,
\n\u2220CDE + \u2220CED + \u2220DCE = 180\u00b0 (\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u092d\u0940 \u0905\u0928\u094d\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u094b \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948)
\n53\u00b0 + 35\u00b0 + \u2220DCE = 180\u00b0
\n\u2220DCE = 180\u00b0 – (53\u00b0 + 35\u00b0) = 180\u00b0 – 88\u00b0= 92\u00b0
\n\u0905\u0924\u0903 \u2220DCE = 92\u00b0<\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4. \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u092f\u0926\u093f \u0930\u0947\u0916\u093e\u090f\u0901 PQ \u0914\u0930 RS \u092c\u093f\u0928\u094d\u0926\u0941 T \u092a\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u0915\u093f \u2220PRT = 40\u00b0, \u2220RPT = 95\u00b0 \u0914\u0930 \u2220TSQ = 75\u00b0 \u0939\u0948,\u00a0<\/strong>\u0924\u094b \u2220SQT \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n\"CBSE
\n\u0939\u0932-<\/strong>
\n\u0394PRT \u092e\u0947\u0902,
\n\u2220PRT + \u2220RPT + \u2220PTR = 180\u00b0 (\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0905\u0928\u094d\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948)
\n40\u00b0 + 95\u00b0 + \u2220PTR = 180\u00b0
\n\u2220PTR = 180\u00b0 – (95\u00b0 + 40\u00b0) = 180\u00b0 – 135\u00b0
\n\u2220PTR = 45\u00b0
\n\u090b\u091c\u0941 \u0930\u0947\u0916\u093e\u090f\u0901 P \u0914\u0930 RS \u092a\u0930\u0938\u094d\u092a\u0930 \u092c\u093f\u0928\u094d\u0926\u0941 T \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902\u0964
\n\u2220QTS = \u2220PIR (\u0936\u0940\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u2220QTS = 45\u00b0 (\u2220PTR = 45\u00b0)
\n\u0905\u092c \u0394QTS \u092e\u0947\u0902,
\n\u2220QTS + \u2220TSQ + \u2220SQT = 180\u00b0 [\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u092d\u0940 \u0905\u0928\u094d\u0924\u0903 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948\u0964]
\n45\u00b0 + 75\u00b0 + \u2220SQT = 180\u00b0
\n\u2220SQT = 180\u00b0 – (45\u00b0 + 75\u00b0) = 180\u00b0 – 120\u00b0 = 60\u00b0
\n\u2220SQT = 60\u00b0<\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u092f\u0926\u093f PQ \u22a5 PS, PQ || SR, \u2220SQR = 28\u00b0 \u0914\u0930 \u2220QRT = 65\u00b0 \u0939\u0948, \u0924\u094b x \u0914\u0930 y \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932-<\/strong>
\n\u0394QRS \u092e\u0947\u0902,
\n\u2220SQR + \u2220QSR = \u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0923 \u2220QRT
\n28\u00b0 + \u2220QSR = 65\u00b0
\n\u2220\u2220QSR = 65\u00b0 – 28\u00b0 = 37\u00b0
\n\u0905\u092c :: PQ || SR \u0914\u0930 QS \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0940 \u0930\u0947\u0916\u093e \u0939\u0948,
\n\u2220PQS = \u2220QSR (\u090f\u0915\u093e\u0928\u094d\u0924\u0930 \u0915\u094b\u0923)
\nx = 37\u00b0 (\u2220PQS = x, \u2220QSR = 37\u00b0)
\nPQ \u22a5 PS
\n\u2220P = 90\u00b0
\n\u0394PQS \u092e\u0947\u0902, \u2220P + \u2220PQS + \u2220PSQ = 180\u00b0 [\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0905\u0928\u094d\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 180\u00b0 \u0939\u094b\u0924\u093e \u0939\u0948\u0964]
\n90\u00b0 + x + y = 180\u00b0
\n\u21d2 x + y = 90\u00b0
\n\u21d2 37\u00b0 + y = 90\u00b0
\n\u21d2 y = 90\u00b0 – 37\u00b0
\n\u21d2 y = 53\u00b0
\n\u0905\u0924\u0903 x = 37\u00b0 \u0924\u0925\u093e y = 53\u00b0<\/p>\n

Ex 6.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6. \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u0394PQR \u0915\u0940 \u092d\u0941\u091c\u093e QR \u0915\u094b P \u092c\u093f\u0928\u094d\u0926\u0941 S \u0924\u0915 \u092c\u0922\u093c\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u2220PQR \u0914\u0930 \u2220PRS \u0915\u0947 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u092c\u093f\u0928\u094d\u0926\u0941 T\u092a\u0930 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902,<\/strong>
\n\u0924\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u2220QTR = \\(\\frac { 1 }{ 2 }\\) QPR \u0939\u0948\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932-<\/strong>
\n\u0394PQR \u092e\u0947\u0902,
\n\u2220PQR + \u2220PRQ + \u2220QPR = 180\u00b0 ……..(1)
\n\u0924\u0925\u093e \u0394TQR \u092e\u0947\u0902,
\n\u2220TQR + \u2220QRT + \u2220QTR = 180\u00b0 ……….(2)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0935 (2) \u0938\u0947,
\n\u2220 TQR + \u2220QRT + \u2220QTR = \u2220PQR + \u2220PRQ + \u2220QPR
\n\u2220TQR + (\u2220 PRQ + \u2220PRT) + \u2220QTR = \u2220PQR + \u2220PRQ + \u2220QPR [\u2220QRT = \u2220PRQ+ \u2220PRT]
\n\u2220TQR + \u2220 PRQ + \u2220PRT + \u2220QTR = \u2220PQR + \u2220PRQ + \u2220QPR
\n\u2220TQR + \u2220PRT + \u2220QTR = \u2220 PQR + \u2220QPR …(3)
\n\u091a\u0942\u0901\u0915\u093f QT, \u2220PQR \u0915\u093e \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948\u0964
\n\u2220TQR = \\(\\frac { 1 }{ 2 }\\) \u2220PQR \u092f\u093e PQR = 2 \u2220TQR ……….(4)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (3) \u0935 \u0938\u092e\u0940\u0915\u0930\u0923 (4) \u0938\u0947,
\n\u2220TQR + \u2220PRT + \u2220QTR = 2 \u2220TQR + \u2220QPR
\n\u2220 PRT + \u2220QTR = \u2220TQR + \u2220QPR …….(5)
\n\u091a\u0942\u0901\u0915\u093f RT, \u2220 PRS \u0915\u093e \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915 \u0939\u0948\u0964
\n\u2220PRT = \\(\\frac { 1 }{ 2 }\\) \u2220PRS
\n\u0914\u0930 \u2220PRS, \u0394PQR \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0923 \u0939\u0948\u0964
\n\u2220PRS = \u2220PQR + \u2220QPR
\n\u2220PRS = 2 \u2220TQR + \u2220QPR ……(6)
\n\u2220PRT = \\(\\frac { 1 }{ 2 }\\) \u2220PRS = \\(\\frac { 1 }{ 2 }\\) (2 \u2220TQR + \u2220QPR)
\n\u2220PRT = \u2220TQR + \\(\\frac { 1 }{ 2 }\\) \u2220QPR
\n\u0938\u092e\u0940\u0915\u0930\u0923 (5) \u092e\u0947\u0902 \u0938\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 (7) \u0915\u094b \u0918\u091f\u093e\u0928\u0947 \u092a\u0930,
\n\u2220QTR = \u2220QPR – \\(\\frac { 1 }{ 2 }\\) \u2220QPR
\n\u2220QTR = \\(\\frac { 1 }{ 2 }\\) \u2220QPR
\n\u0907\u0924\u093f \u0938\u093f\u0926\u094d\u0927\u092e.<\/p>\n

Hope given NCERT Solutions for Class 9 Maths Chapter 6 are helpful to complete your homework.<\/p>\n","protected":false},"excerpt":{"rendered":"

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (\u0930\u0947\u0916\u093e\u090f\u0901 \u0914\u0930 \u0915\u094b\u0923) (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 6 Lines and Angles. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.1 Ex 6.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u00a0\u0906\u0915\u0943\u0924\u093f. 6.13 …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Hindi Medium)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":7719,"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 6 Lines and Angles (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-6-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 6 Lines and Angles (Hindi Medium) - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (\u0930\u0947\u0916\u093e\u090f\u0901 \u0914\u0930 \u0915\u094b\u0923) (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 6 Lines and Angles. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.1 Ex 6.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u00a0\u0906\u0915\u0943\u0924\u093f. 6.13 … NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Hindi Medium) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-6-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=\"2021-07-23T04:50:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-07-23T12:07:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-6-Lines-and-Angles-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=\"4 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-6-hindi\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-6-Lines-and-Angles-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-6-Lines-and-Angles-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"width\":1280,\"height\":720,\"caption\":\"NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Hindi Medium)\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-6-hindi\/#webpage\",\"url\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-6-hindi\/\",\"name\":\"NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Hindi Medium) - 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