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  • If AB = QR, BC = PR and CA = PQ, then (A) triangle DABC cong triangle PQR (B) triangle CBA cong triangle PRQ (C) triangle BAC cong triangle RPQ (D) triangle PQR cong triangle BCA

If AB = QR, BC = PR and CA = PQ, then
\\(A) \triangle ABC \cong \triangle PQR \\ (B) \triangle CBA \cong \triangle PRQ\\ (C) \triangle BAC \cong \triangle RPQ\\ (D) \triangle PQR \cong \triangle BCA\\

Answers (1)

[B]

Solution.         AB = QR, BC =PR, CA = PQ (Given)

Triangles follow the SSS criterion for congruence

In option (A) \triangle ABC \cong \triangle PQR, from this we conclude that side AB = PQ

But it is given AB = QR and AB = PQ may or may not be possible

In option(C) \triangle BCA \cong \triangle RPQ, by same relation, we say that

side BA = RP may or may not be possible because it is given BA = QP

In option (D) \triangle PQR \cong \triangle BCA

side PQ = BC may or may not be possible

In option (B) \triangle CBA \cong \triangle PQR,

CB = PR, BA = RQ, AC = QP (all are given.)

Hence option (B) is correct.

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infoexpert24

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