Maths-
General
Easy
Question
Prove that ∠PRS ≅ ∠PSR
Hint:
Use supplementary angles property.
The correct answer is: ∠ PRS ≅ ∠ PSR
Complete step by step solution:
Consider 2 triangles, and
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, ⇒ ∠ PRS = ∠ PSR
Ie, Since ∠ PRQ = ∠ PST, we have
∠ PRS = 180°- ∠ PRQ (Supplementary angles) and
∠PSR=180° - ∠PST=180° - ∠ PRQ (Supplementary angles)
Hence, ∠ PRS ≅ ∠ PSR
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