Question

Q.Prove that a line drawn through the midpoint of one side of a triangle parallel to another

side bisects the third side.
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Answer 1

Step-by-step explanation:

Given that ABC is a traingle and D and E are mid points of traingle. Construction : Join C and D , B and E. Prove that : DE // BC.Proof :  In ΔADE = ΔBDE AD = BD ( D is mid point) DE = DE ( same height) Area of ΔADE = Area of ΔBDE -------------(1) In ΔADE = ΔCDE AE = EC ( E is mid point) DE = DE ( same height) Area of ΔADE = Area of ΔCDE -------------(2)from (1) and (2) we get  Area of ΔBDE = Area of ΔCDE ∴ DE // BC.

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