In the given figure, AB = AC, P, Q and R are mid-points of sides BC, CA and AB respectively, then △ PQR is :

1. scalene

2. isosceles

3. equilateral

4. obtuse angled

Given,

AB = AC = x (let)

From figure,

AR = RB, BP = PC and AQ = QC.

∴ R, P and Q are mid-points of sides AB, BC and AC respectively.

Join QR.

By mid-point theorem,

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

∴ PQ = $\dfrac{1}{2}AB = \dfrac{x}{2}$, PR = $\dfrac{1}{2}AC = \dfrac{x}{2}$ and QR = $\dfrac{1}{2}BC$.

In △ PQR,

PQ = PR.

∴ △ PQR is an isosceles triangle.

Hence, Option 2 is the correct option.