Question 37 (iii) (B) - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 19, 2024 by Teachoo

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Question 37 (iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that △ ABM ∼ △ DEN.Given AM & DN are medians Since AM is median, M is mid-point of BC ∴ BM = CM = 𝟏/𝟐 BC Also, DN is median, N is mid-point of EF ∴ EN = FN = 𝟏/𝟐 EF We are assuming △ ABC ∼ △ DEF Otherwise this question cannot be solved Since △ ABC ∼ △ DEF And, Sides of similar triangles are proportional So, 𝐴𝐵/𝐷𝐸=𝐴𝐶/𝐷𝐹=𝐵𝐶/𝐸𝐹 𝐴𝐵/𝐷𝐸=𝐵𝐶/𝐸𝐹 Putting BC = 2BM, and EF = 2EN 𝐴𝐵/𝐷𝐸=2𝐵𝑀/2𝐸𝑁 𝑨𝑩/𝑫𝑬=𝑩𝑴/𝑬𝑵 Also, since △ ABC ∼ △ DEF And, corresponding angles of similar triangles are equal ∴ ∠ B = ∠ E Now, In Δ ABM & ΔDEN ∠𝐵=∠𝐸 𝐴𝐵/𝐷𝐸=𝐵𝑀/𝐸𝑁 Hence by SAS similarly ΔABM ∼ ΔDEN Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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