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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