Question

DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal area. prove that the diagonal DF bisect GE.

Answer 1

Given : DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas  

To Find : Prove that diagonal DF bisects GE also .

Solution :

diagonal DF divides it into two parts of equal areas

=> Area of ΔDFG  =  Area of ΔDFE

Draw GM ⊥  DF  and EN ⊥  DF

=> (1/2) GM * DF  = (1/2) EN * DF

=> GM = EN

Let say GF & DF intersect at O

Now comparing

ΔGOM  & Δ EON

∠GOM  = ∠EON  ( vertically opposite angles)

∠GMO = ∠ENO  = 90°

GM = EN   ( shown above)

hence ΔGOM  ≅ Δ EON    ( RHS)

=> GO = EO

Hence diagonal DF bisects GE

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