In figure, side QR of ΔPQR is produced on both sides such that ∠PQS=∠PRT. Prove that PQ=PR.
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In ΔPQR ∠PQS+∠PQR=1800 (linear pair angles) ∠PQS+∠q=1800 ∠q=1800–∠PQS …(i) Also ∠r=1800–∠PRT …(ii) But ∠PQS=∠PRT (given) …(iii) From (iii), eqn (i) becomes ∠q=1800–∠PRT …(iv) Now from (ii) and (iv), we have ∠q=∠r i.e., ∠PQR=∠PRQ PR=PQ (converse of isosceles A theorem) Hence proved.