Consider parallelogram PQRS, where PQ ≅ RS and QR ≅ PS. Construct diagonal PR and diagonal QS. By the SSS criterion, ΔPQR ≅ ΔRSP

Question

3 years ago

14

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.

Mathematics

2 answers:

Reptile [31] · Answer 1 · 2023-02-26T09:31:15+03:00

Reptile [31]3 years ago

8 0

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

Katarina [22] · Answer 2 · 2023-02-26T11:06:43+03:00

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

<h3>What is Parallelogram?</h3>

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

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