Question

In the figure, Angle R = Angle S, and Angle RPQ = Angle PQS. prove that PS = QR brainly PLEASE BE FAST​

Answer 1

★ Given :-

1. ∠R = ∠S
2. ∠RPQ = ∠SQP

★ To prove :-

PS = QR

★ Solution :-

First, let's consider Triangles ∆PSQ and ∆PRQ

In ∆PSQ and ∆PRQ,

• ∠PSQ = ∠PRQ [Given]

• ∠SQP = ∠RPQ [Given]

• PQ = QP [Common side]

So, By AAS congruency,

∆PSQ ≅ ∆PRQ

Now,

We know that;

Corresponding parts of congruent trianngles (CPCT) are equal.

∴ PS = QR

Know more:

• We say 2 triangles are congruent by AAS congruency when any 2 angles and 1 side are equal.
• We say 2 triangles are congruent by ASA congruency when 2 angles and the included side between the angles are equal.

Answer 2

Triangle PSQ and Triangle PRQ

In the triangle PSQ and Triangle PRQ

=> <PSQ =<PRQ

=><SQP=<RPQ

=>PQ=QP

So triangle PSQ =~triangle PRQ

The corresponding parts are equal

So PS=QR