Question

In triangle pqr the sides qp and rp have been produced to s and t such that pq =ps pr =pt. Prove that the segment qr parallel to st

Answer 1

QS = RT? Then only we can prove that tri PQR is an isosceles triangle. PROOF: In triangle PQS & tri PRT,

Since, QS = RT< QSP = < RTP (each being 90°) & < P = < P (common angles)=> tri PQS congruent to tri PRT ( AAS similarity corollary)=> PQ = PR ( cpct). Hence, tri PQR is an isosceles triangle. Hence proved.

Answer 2

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