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 Oct. 3, 2024 by Teachoo
Question 37 (iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that β³ ABM βΌ β³ DEN.Given AM & DN are medians Since AM is median, M is mid-point of BC β΄ BM = CM = π/π BC Also, DN is median, N is mid-point of EF β΄ EN = FN = π/π EF We are assuming β³ ABC βΌ β³ DEF Otherwise this question cannot be solved Since β³ ABC βΌ β³ DEF And, Sides of similar triangles are proportional So, π΄π΅/π·πΈ=π΄πΆ/π·πΉ=π΅πΆ/πΈπΉ π΄π΅/π·πΈ=π΅πΆ/πΈπΉ Putting BC = 2BM, and EF = 2EN π΄π΅/π·πΈ=2π΅π/2πΈπ π¨π©/π«π¬=π©π΄/π¬π΅ Also, since β³ ABC βΌ β³ DEF And, corresponding angles of similar triangles are equal β΄ β B = β E Now, In Ξ ABM & ΞDEN β π΅=β πΈ π΄π΅/π·πΈ=π΅π/πΈπ Hence by SAS similarly ΞABM βΌ ΞDEN Hence proved
