# 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 .

2
by ayush16

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by ayush16

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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..

Now, ar (Δ ABC) = ar (ΔDBC)

1/2 * AE * BC = 1/2 * DE * BC

so, AE = DE

∴ BC bisects AD