CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at August 6, 2026 by Teachoo
Transcript
Question 37 (iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that ā³ ABM ā¼ ā³ DEN.Given AM & DN are medians Since AM is median, M is mid-point of BC ā“ BM = CM = š/š BC Also, DN is median, N is mid-point of EF ā“ EN = FN = š/š EF We are assuming ā³ ABC ā¼ ā³ DEF Otherwise this question cannot be solved Since ā³ ABC ā¼ ā³ DEF And, Sides of similar triangles are proportional So, š“šµ/š·šø=š“š¶/š·š¹=šµš¶/šøš¹ š“šµ/š·šø=šµš¶/šøš¹ Putting BC = 2BM, and EF = 2EN š“šµ/š·šø=2šµš/2šøš šØš©/š«š¬=š©š“/š¬šµ Also, since ā³ ABC ā¼ ā³ DEF And, corresponding angles of similar triangles are equal ā“ ā B = ā E Now, In Ī ABM & ĪDEN ā šµ=ā šø š“šµ/š·šø=šµš/šøš Hence by SAS similarly ĪABM ā¼ ĪDEN Hence proved
