{"id":27784,"date":"2021-07-01T17:50:01","date_gmt":"2021-07-01T12:20:01","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=27784"},"modified":"2021-07-01T17:53:28","modified_gmt":"2021-07-01T12:23:28","slug":"ncert-solutions-for-class-10-maths-chapter-6-ex-6-4","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-10-maths-chapter-6-ex-6-4\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4"},"content":{"rendered":"

These NCERT Solutions for Class 10 Maths<\/a> Chapter 6 Triangles Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.4<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nLet \u2206ABC ~ \u2206DEF and their areas be, respectively, 64 cm\u00b2 and 121 cm\u00b2. If EF = 15.4 cm, find BC.
\nSolution:
\nSince, \u2206ABC ~ \u2206DEF
\nThe ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
\n\"NCERT<\/p>\n

Question 2.
\nDiagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
\nSolution:
\nABCD is a trapezium with AB || DC and AB = 2 CD
\n\"NCERT<\/p>\n

Question 3.
\nIn the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that \"NCERT
\n\"NCERT
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nIf the areas of two similar triangles are equal, prove that they are congruent.
\nSolution:
\nGiven : Areas of two similar triangles are equal.
\nTo Prove : Triangles are congruent. Ratio in the areas of two similar triangles is equal to the ratio of their respective sides.
\nProof: Let \u2206ABC and \u2206PQR be two triangles.
\n\"NCERT
\nHence, by SSS congruence theorem
\n\u2206 ABC \u2245 \u2206PQR (Proved)<\/p>\n

Question 5.
\nD, E and F are respectively the mid-points of sides AB, BC and CA of \u2206ABC. Find the ratio of the areas of \u2206DEF and \u2206ABC.
\nSolution:
\nABC is a triangle and D, E, F are the mid\u00acpoints of the sides AB, BC and CA respectively
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nProve that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
\nSolution:
\nGiven \u2206 ABC ~ \u2206DEF, and AP and DQ are their medians.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nProve that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
\nSolution:
\nGiven A square ABCD. Equilateral ABCE and AACF have been described on side BC diagonal AC respectively.
\n\"NCERT<\/p>\n

Question 8.
\nABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is _________.
\n(a) 2 : 1
\n(b) 1 : 2
\n(c) 4 : 1
\n(d) 1 : 4
\nSolution:
\n(c) 4 : 1<\/p>\n

\"NCERT<\/p>\n

Question 9.
\nSides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio __________.
\n(a) 2 : 3
\n(b) 4 : 9
\n(c) 81 : 16
\n(d) 16 : 81
\nSolution:
\n(d) 16 : 81<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.4 Question 1. Let \u2206ABC ~ \u2206DEF and their areas be, respectively, 64 cm\u00b2 and 121 cm\u00b2. If EF = 15.4 cm, …<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 - 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-10-maths-chapter-6-ex-6-4\/\" \/>\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 10 Maths Chapter 6 Triangles Ex 6.4 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts. 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If EF = 15.4 cm, … NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-10-maths-chapter-6-ex-6-4\/\" \/>\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=\"2021-07-01T12:20:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-07-01T12:23:28+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/ncertsolutions.guru\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\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=\"5 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-10-maths-chapter-6-ex-6-4\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-10-maths-chapter-6-ex-6-4\/#webpage\",\"url\":\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-10-maths-chapter-6-ex-6-4\/\",\"name\":\"NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 - 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