Question

Consider parallelogram PQRS, where PQ ≅ RS and QR ≅ PS. Construct diagonal PR and diagonal QS. By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ. Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
What statement is proven by the given steps?

A.
A quadrilateral with congruent consecutive angles is a parallelogram.
B.
Consecutive angles of a parallelogram are congruent.
C.
Opposite angles of a parallelogram are congruent.
D.
A quadrilateral with congruent opposite angles is a parallelogram.

Answer 1

Answer: C. Opposite angles of a parallelogram are congruent.

Answer 2

The correct answer would be option(C) opposite angles of a parallelogram are congruent.

What is Parallelogram?

A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.

Given that PQRS is a parallelogram.

PQ ≅ RS

QR ≅ PS

By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.

Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.

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