In Figure `(P S)/(S Q)=(P T)/(T R)`and `/_P S T=/_P R Q`. Prove that P – InterviewSolution

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1.	In Figure `(P S)/(S Q)=(P T)/(T R)`and `/_P S T=/_P R Q`. Prove that PQR is an isosceles triangle.
Answer» Here, we are given, `(PS)/(SQ) = (PT)/(TR)` As, ST is dividing two sides of triangle in equal ratio, it will be parallel to third side. So, `ST \|\|QR` That means, `/_PST = /_PQR` We are given,`/_PST = /_PRQ` So, `/_PRQ = /_PQR` As two angles of triangle `Delta PQR` are equal, it is an isosceles triangle.

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