Question

State True or False

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed ( see Fig.)Then ar (ABCD) = ar (PBQR) .

• A. True
• B. False

Answer 1

The correct option is A True

Join AC and QP

Then Triangle ACQ and triangle APQ are between same base and parallels

Therefore,

$Ar\left(\Delta ACQ\right)=Ar\left(\Delta APQ\right)$

Subtracting $Ar\left(\Delta ABQ\right)$ from it we get,

$Ar\left(\Delta ACB\right)=Ar\left(\Delta BPQ\right)$

Therefore $Ar\left(ABCD\right)=Ar\left(PBQR\right)$ (Double of ACB and BPQ)