Mathematics
In the adjoining figure, PQ || BA and RS || CA. If BP = RC, prove that:
(i) △BSR ≅ △PQC
(ii) BS = PQ
(iii) RS = CQ.
Triangles
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Answer
Given, BP = RC
⇒ BR - PR = PC - PR
⇒ BR = PC.
Now, in △BSR and △PQC,
∠B = ∠P (Corresponding angles)
∠R = ∠C (Corresponding angles)
BR = PC (Proved)
Hence, proved △BSR ≅ △PQC by ASA axiom.
(ii) We know that corresponding parts of congruent triangles are equal.
∴ BS = PQ.
(iii) We know that corresponding parts of congruent triangles are equal.
∴ RS = CQ.
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