Question

DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas.Prove that the diagonal DF bisects GE.

Answer 1

since ar(∆DEF)=ar(∆DGE).so they must be congruent. and by the congruence law ,DF=GE.now in triangles DOE and GOF, we have ( consider O as the midpoint of DF),DE=GF
or, <DOE=<GOE (vertically opposite angles)
or, DO=OF.so
∆DOE congruent to ∆GOF
and thus EO=GE.hence DF bisects GE