In Figure `(P S)/(S Q)=(P T)/(T R)`and `/_P S T=/_P R Q`. Prove that PQR is an isosceles triangle.
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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.