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  • In Fig., ABCD and AEFD are two parallelograms. Prove that ar (PEA) = ar (QFD)

ABCD and AEFD are two parallelograms. Prove that ar (PEA) $=\operatorname{ar}($ QFD $)$

 

Answers (1)

Solution.

Given: Two parallelograms ABCD and AEFD.

To prove: $\operatorname{ar}(\triangle P E A)=\operatorname{ar}(\triangle Q F D)$

Proof:

PQDA is a parallelogram, so $A P\|D Q, P Q\| A D$

Now, parallelograms PQDA and AEFD are on the same base AD and lie between the same parallel lines AD and EQ .

Hence,

$
\begin{aligned}
& \operatorname{ar}(\| g m P Q D A)=\operatorname{ar}(\| g m A E F D) \\
& \operatorname{ar}(P F D A)+\operatorname{ar}(\triangle Q F D)=\operatorname{ar}(\triangle P E A)+\operatorname{ar}(P F D A)
\end{aligned}
$

So, we get:

$
\operatorname{ar}(\triangle Q F D)=\operatorname{ar}(\triangle P E A)
$

Hence proved

 

Posted by

infoexpert26

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