In △ ABC and △ PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q; then triangles are :

1. isosceles but not congruent

2. isosceles and congruent

3. congruent but not isosceles

4. neither isosceles nor congruent.

△ ABC and △ PQR are shown below:

In △ ABC,

⇒ AB = AC (Given)

∴ ∠C = ∠B = x (let) (Angles opposite to equal sides are equal).

Given,

⇒ ∠P = ∠C

∴ ∠P = x.

⇒ ∠Q = ∠B

∴ ∠Q = x.

In △ PQR,

⇒ ∠P = ∠Q = x

⇒ QR = PR (Sides opposite to equal angles are equal).

∴ ABC and PQR are isosceles triangles.

Hence, Option 1 is the correct option.