Question

D and E are position on sides AB and AC respectively of triangle ABC such that ar(triangle DBC) = ar (triangle EBC ) prove that (DE !!BC)

Answer 1

area (DBC) = area (EBC)

We know that Area of Any triangle is
1/2*b*h


Since, Area of ΔDBC and ΔEBC are same and Base is common for both the triangles

⇒ height of ΔDBC is also equal to the height of ΔBEC

⇒ h1 = h2



Hence BC || DE

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Answer 2

see the attachment for answer