The image of the problem is attached below.
Given triangle PQR is an equilateral triangle.
i.e PQ = PR.
To prove that angles opposite to equal sides are equal.
i.e to prove ∠Q = ∠R.
Construction: Draw a bisector of ∠P intersecting QR at S.
In ΔPQS and ΔPRS,
PQ = PR (equal side)
∠QPS = ∠SPR (bisecting angle)
PS = PS (common side)
∴ ΔPQS ≅ ΔPRS (by SAS congruence rule)
Corresponding parts of congruence triangles equal.
⇒ ∠PQS = ∠PRS
i.e ∠Q = ∠R
Hence angles opposite to equal sides of an equilateral triangle are equal.
