Question

D and E are points on sides AB and AC respectively of A ABC such that ar (DBC)=ar (EBC). Prove that DE|| BC.
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Answer 1

Answer:

Given that ar (DBC) = ar (EBC)

Since ΔEBC and ΔDBC are lying on a common base BC and they also have equal areas, therefore, ΔEBC and ΔDBC will lie between the same parallel lines.

Hence, DE || BC proved.

Answer 2

Answer:

Given thatDandE

are points on sides ABandACrespectively of△ABC

such that

ar.(△DBC)=

ar.(△EBC)

To Prove:

DE∥

BC

.

Construction: Join

BE

and

DC

.

Proof:

ar.(△DBC)=

ar.(△EBC)

BC∥

DE

△DBC and △EBC are on base BC .

Hence, proved.