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In ΔABC and ΔPQR, if AB = AC, ∠C =∠P and ∠B = ∠Q, then the two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but not isosceles
(d) Neither congruent nor isosceles
(a) $\ln \triangle A B C$, $A B=A C$ [given]
$\Rightarrow \quad \angle C=\angle B \quad$ [angles opposite to equal sides are equal]
So, $\triangle A B C$ is an isosceles triangle.
But it is given that, $\angle B=\angle Q$
$\angle C=\angle P$
$\therefore \quad \angle P=\angle Q \quad[\because \angle C=\angle B]$
$\Rightarrow \quad Q R=P R \quad$ [sides opposite to equal angles are equal]
So, $\triangle P Q R$ is also an isosceles triangle.
Therefore, both triangles are isosceles but not congruent. As, we know that AAA is not a criterion for congruence of triangles.