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.

Question

contestada

Respuesta :

Medunno13 Medunno13 · Answer 1 · 2022-07-19T15:57:11+02:00

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

Answer Link

saimaparvezVT saimaparvezVT · Answer 2 · 2022-07-28T11:55:04+02:00

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

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.

Learn more about parallelogram here:

brainly.com/question/11220936

#SPJ5