DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas . Prove that diagonal DF bisects GE also . Share with your friends Share 17 Akhil Goyal answered this Consider the diagram below: Let GA, EB pe perpendiculars on DF from G, E respectively.Given:ar(△DEF)=ar(△DGF)⇒12(DF)(GA)=12(DF)(EB)⇒GA=EB -------------(1)Also, ∠GAO=∠EBO=90∘ -----(2)Further, ∠AOG=∠BOE (vertically opposite angles)Now, ∠AGO=180∘-∠GAO-∠AOGSimilarly, ∠BEO=180∘-∠EBO-∠BOETherefore, ∠AGO=∠BEO ------(3)Using (1), (2), (3), we can see that △GOA≅△BOE (by ASA property)Hence, GO=EO. 44 View Full Answer