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TRIANGLE A B C and D B C are on the same base BC with A ,D on opposit side of BC , such that ar (triangle ABC )equal ar (DBC ).Show that BC bisect AD .

GIVEN- ar triangle ABC= ar triangle DBC They have same base BC and have same area. TPT- BC bisects AD construction- let AO be the height of triangle ABC and let DO be the height of triangle DBC. PROOF- In triangle ABC and DBC They have same bases and equal area that is 1/2 X BC X AO =1/2 X BC X DO As area triangle ABC = ar triangle DBC Therefore AO=DO Therefore BC bisects AD. Hence proved..