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:**

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

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