Question

PQRS is a parallelogram if the two diagonals are equal then the measure of angle PQR is​

Answer 1

Given : PQRS is a parallelogram

two diagonals are equal

To Find : the measure of angle PQR

Solution:

A parallelogram with equal diagonals is a rectangle

And all angles of a rectangle are right angles

Hence m∠PQR is 90°

Proof:

Compare ΔPQR  and ΔQPS

PQ  ≅  QP   using reflexive property of congruence

QR ≅ PS     Opposite sides of parallelogram

PR ≅ QS       Given that Diagonals are equal

=> ΔPQR  ≅ ΔQPS   (SSS congruence)

=> ∠PQR = ∠QPS

Sum of adjacent angles of a parallogram is 180°

=> ∠PQR + ∠QPS = 180°

Hence ∠PQR = ∠QPS = 90°

m∠PQR is 90°

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