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D and E are points on sides AB and AC respectively of ABC suc

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$D$ and $E$ are points on sides $A B$ and $A C$ respectively of $△ A BC$ such that $a r (△ BC D) = a r (△ BCE)$ . Prove that $D E ∣∣ BC$ .

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D

and

E

are points on sides

A B

and

A C

respectively of

△ A BC

such that

a r (△ BC D) = a r (△ BCE)

. Prove that

D E ∣∣ BC

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Text solutionVerified

Given D and E are point on sides AB and AC respectively of triangle ABC such that Area(ΔBCD) = Area(ΔBCE).

Given that Area(ΔBCD) = Area(ΔBCE).

Then the height of triangle BCD and Triangle BCE are the same because both triangles are the same

Then it possible that both triangle on the same base and between parallel line BC and DE

Therefore, they will lie between the same parallel lines.

∴BC∥DE [henceproved]

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Question Text	$D$ and $E$ are points on sides $A B$ and $A C$ respectively of $△ A BC$ such that $a r (△ BC D) = a r (△ BCE)$ . Prove that $D E ∣∣ BC$ .
Answer Type	Text solution:1
Upvotes	150