Question

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 .

Answer 1

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..

THANKS FOR ASKING

Answer 2

let ABC and DBC be two triangles with AE passes through BC to D
Now,  ar (Δ ABC) = ar (ΔDBC)
             1/2 * AE * BC = 1/2 * DE * BC
           so, AE = DE
∴ BC bisects AD