In ∆ABC and ∆PQR, it is given that AB = AC,
Question:

In ABC and ∆PQR, it is given that 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

Solution:

(a) isosceles but not congruent

$A B=A C$

$\Rightarrow \angle C=\angle B$

$\Rightarrow \angle P=\angle Q \quad[\because \angle C=\angle P$ and $\angle B=\angle Q]$

Thus, both the triangles are isosceles but not congruent.