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CBSE Class 9 Answered

In fig., in PQR, right angled at P. PS is perpendicular to QR. Prove that QPS = PRQ.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Given: In PQR, right at P. PS is perpendicular to QR.

To prove: QPS = PRQ

Proof:

In QPS, QPS + PSQ + PQS = 180o

QPS + 90o + PQS = 180o

QPS = 90o - PQS

QPS = 90o - Q ...(i)

In PQR

P + Q + R = 180o

Q + R = 180o - P = 180o - 90o = 90o

Or, R = 90o - Q ...(ii)

(i) and (ii) QPS = PRQ.

Answered by | 04 Jun, 2014, 03:23: PM

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