S is a point on side QR of a triangle PQR such that PS=PR. Prove that PQ is greater than PS
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In triangle PQR:
PS=PR
So,
∠PSR=PQR
IN ΔPRS :
∠PRS+∠RPS=∠PSQ(∴ΔPSQ will become an obtuse angled triangle with ∠PSQ as the obtuse angle)
So the line PQ will be longer than line PS as
According to the The angles ∠PRS AND ∠RPS will be smaller than ∠PSQ.
PS=PR
So,
∠PSR=PQR
IN ΔPRS :
∠PRS+∠RPS=∠PSQ(∴ΔPSQ will become an obtuse angled triangle with ∠PSQ as the obtuse angle)
So the line PQ will be longer than line PS as
According to the The angles ∠PRS AND ∠RPS will be smaller than ∠PSQ.
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