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Question
Equal sides QP and RP of an isosceles ΔPQR are produced beyond P to S and T such that ΔPST is an isosceles triangle with PS = PT. Prove that TQ = SR.
Sum
Solution
In ΔPTQ and ΔPSR
PQ = PR ...(given)
PT = PS ...(given)
∠TPQ = ∠SPR ...(vertically opposite angles)
Therefore, ΔPTQ ≅ ΔPSR
Hence, TQ = SR.
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