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

Answer 1

(a) isosceles but not congruent

$$\begin{gathered} AB=AC \\ \Rightarrow \angle C=\angle B \\ \Rightarrow \angle P=\angle Q[\because \angle C=\angle P\mathrm{and}\angle B=\angle Q] \end{gathered}$$
Thus, both the triangles are isosceles but not congruent.