Question

In the figure given below, two parallelograms ABCD and PQCD lie on the same base CD and between the same parallel lines AQ and CD. Then, $△APD$ and $△BQC$ are congruent

• A. True
• B. False

Answer 1

The correct option is A

True

In $△APD$ and $△BQC$

$\angle PAD=\angle QBC$ (corresponding angles)

AD = BC ( opp. sides of parallelogram)

$\angle APD=\angle BQC$ (corresponding angles)

$△APD\cong △BQC$ (by ASA criterion)

Also, we can obtain congruency by SSS criterion.

ABCD is a parallelogram.
Hence, AD = BC ------ (1)
and AB = CD -------- (2)

PQCD is a parallelogram
Hence, PD = QC ------- (3)
and PQ = CD ------- (4)

From (2) and (4)

AB = PQ
subtracting PB on both sides, we get
AB - PB = PQ - PB
AP = BQ ---- (5)

From (1), (3) and (5), we have
$△APD\cong △BQC$ (By SSS criterion)