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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 $A B=Q R, B C=P R$ and $C A=P Q$, then
(A) $\triangle A B C \cong \triangle P Q R$
(B) $\triangle C B A \cong \triangle P R Q$
(C) $\triangle B A C \cong \triangle R P Q$
(D) $\triangle P Q R \cong \triangle B C A$

Answers (1)

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

Triangles follow the SSS criterion for congruence

In option (A) $\triangle A B C \cong \triangle P Q R$, from this, we conclude that side $\mathrm{AB}=\mathrm{PQ}$

But it is given $A B=Q R$ and $A B=P Q$ may or may not be possible

In option (C) $\triangle B C A \cong \triangle R P Q$, by the same relation, we say that

side $B A=R P$ may or may not be possible because it is given $B A=Q P$

In option (D) $\triangle P Q R \cong \triangle B C A$

side $P Q=B C$ may or may not be possible

In option (B) $\triangle C B A \cong \triangle P Q R$,

$C B=P R, B A=R Q, A C=Q P$ (all are given.)

Hence option (B) is correct.

Posted by

infoexpert24

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