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Ex 9.3, 2 - In triangle ABC, E is mid-point of median AD - Ex 9.3

Ex 9.3, 2 - Chapter 9 Class 9 Areas of Parallelograms and Triangles - Part 2

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Ex 9.3, 2 In a triangle ABC , E is the mid-point of median AD show that ar(BED) = 1/4 ar (ABC). Given: Δ ABC, with AD as median i.e. BD = CD & E is the mid-point of AD, i.e., AE = DE To prove: ar (BED) = 1/4 ar (ABC). Proof : AD is a median of Δ ABC & median divides a triangle into two triangles of equal area ∴ ar (ABD) = ar (ACD) ⇒ ar (ABD) = 1/2 ar (ABC) In Δ ABD, BE is the median median divides a triangle into two triangles of equal area ∴ ar (BED) = ar (BEA) ⇒ ar (BED) = 1/2 ar (ABD) ⇒ ar (BED) = 1/2× 1/2 ar (ABC) ⇒ ar (BED) = 1/4 ar (ABC) 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.