# Sides Opposite to the Equal Angles of a Triangle are Equal

Here we will prove that the sides opposite to the equal angles of a triangle are equal.

Given: In ∆ABC, ∠XYZ = ∠XZY.

To prove: XY = XZ.

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.

Proof:

 Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM(ii) ∠YXM = ∠ZXM(iii) XM = XM.2. ∆XYM ≅ ∆XZM 3. XY = XZ. (Proved) Reason1. (i) Given.(ii) XM bisects ∠YXZ.(iii) Common side.2. By AAS criterion. 3. CPCTC.

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