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प्रश्न
In ΔPQR, S and T are points on PQ and PR respectively. `(PS)/(SQ) = (PT)/(TR)` and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.
उत्तर
Given `(PS)/(SQ) = (PT)/(TR)`
∠PST = ∠PRQ
To prove : PQR is an isosceles triangle
Proof : `(PS)/(SQ) = (PT)/(TR)`
∠PST = ∠PQR ...(Corresponding angles)
But ∠PST = ∠PRQ
∠PQR = ∠PRQ
PR = PQ ...(Sides opposite to equal angles are equal)
ΔPQR is isosceles triangle.
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