D and E are points on sides AB and AC respectively of triangle ABC such that ar(DBC) $=$ ar(EBC) then DE||BC.

True

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False

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Solution

The correct option is A True
Area of $△ D B C = \frac{1}{2} \times B C \times h_{1}$ ....... $(1)$
Area of $△ E B C = \frac{1}{2} \times B C \times h_{2}$ ....... $(2)$
Given:Area of $△ D B C =$ Area of $△ E B C$
$\Rightarrow \frac{1}{2} \times B C \times h_{1} = \frac{1}{2} \times B C \times h_{2}$
$\Rightarrow h_{1} = h_{2}$
So, distance of point $D$ from line $B C$ is same as the distance of point $E$ from line $B C$
So,line $D E ∥ B C$
$∵$ distance between parallel lines are same.

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Similar questions

Q. If

D

and

E

are points on side

A B

and

A C

respectively of triangle

A B C

such that

a r (Δ D B C) = a r (Δ E B C)

, then prove that

D E ∥ B C

D and E are points on sides AB and AC respectively of ΔABC such that

ar (DBC) = ar (EBC). Prove that DE || BC.

If D and E are points on sides AB and AC respectively of $△$ ABC such that ar ( $△$ DBC) = ar ( $△$ EBC), then DE $∥$ BC.

D and E are points on the sides AB and AC, respectively, of $△$ ABC such that DE || BC and DE divides $△$ ABC into two parts that are equal in area. Find $\frac{B D}{A B}$ .

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and

E

are points on sides

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and

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respectively of

△ A B C

such that

a r e a (D B C) = a r e a (E B C)

. Prove that

D E ∥ B C

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

D and E are points on sides AB and AC respectively of triangle ABC such that ar(DBC) $=$ ar(EBC) then DE||BC.