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State true or false.

In the figure given below, $A B C D$ and $A E F D$ and are two parallelograms. Then $ar(Δ APE):ar(Δ PFA)= ar(Δ QFD):ar(Δ PFD)$ are two parallelograms. Then .

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True

False

answer is A.

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Detailed Solution

Given that,

A B C D

and

A E F D

are two parallelograms.
Question Image

Δ APE

and

Δ DQF

stand on same base

P E

and FQ lie between the same parallel EQ and

A D

. So,

a r Δ A P E = a r Δ D Q F

……..(1)
Join PD.
Question Image

Since,

P F

lie between the same parallel

P Q

and

A D

.
Therefore,

a r Δ P F A = a r Δ P F D

…….(2)
Divide the equation (1) by (2),

\frac{area (ΔAPE)}{area (ΔPFA)} = \frac{area (ΔQFD)}{area (ΔPFD)}

Analyze that,

ar(Δ APE):ar(Δ PFA)= ar(Δ QFD):ar(Δ PFD)

Hence, the statement is true.
Therefore, option 1 is correct.

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