Question 5:
In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ.
Answer:
As PR > PQ,
∠PQR > ∠PRQ (Angle opposite to larger side is larger) … (1)
PS is the bisector of ∠QPR.
∠QPS = ∠RPS … (2)
∠PSR is the exterior angle of ∆PQS.
∠PSR = ∠PQR + ∠QPS … (3)
∠PSQ is the exterior angle of &PRS.
∠PSQ = ∠PRQ + ∠RPS … (4)
Adding equations (1) and (2), we obtain
∠PQR + ∠QPS > ∠PRQ + ∠RPS
∠PSR > ∠PSQ [Using the values of equations (3) and (4)]
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