Maths-

General

Easy

Question

# Explain how you can prove PR = PS.

Hint:

### Use supplementary angles property.

## The correct answer is: PR = PS (corresponding parts of congruent triangles)

### Complete step by step solution:

Consider 2 triangles, △ PQRand △ PTS

From the figure, we have

∠ PQR = ∠ PTS (given)

∠ QPR = ∠ TPS (given)

By angle sum property,

We have, ∠ PRQ = ∠ PST

Ie, ∠ PRQ = 180° - (∠ PQR + ∠ QPR) and

∠ PST = 180° - (∠ PTS + ∠ TPS) = 180°- (∠ PQR + ∠ QPR)

So, ⇒ ∠ PRQ = ∠ PST

Now we have,

∠ PQR = ∠ PTS (given)

QR = TS ( given)

∠ PRQ = ∠ PST (proved)

So, △ PQR ≅ △ PTS by ASA congruence rule.

⇒ PR = PS (corresponding parts of congruent triangles)

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