Here we will prove that in an isosceles triangle, the angles opposite to the equal sides are equal.

**Solution:**

**Given:** In the isosceles ∆XYZ, XY = XZ.

**To prove** ∠XYZ = ∠XZY.

**Construction:** Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.

**Proof:**

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

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