Here we will prove that in an isosceles triangle, the angles opposite to the equal sides are equal.
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.
1. In ∆XYM and ∆XZM,
(i) XY = XZ
(ii) XM = XM
(iii) ∠YXM = ∠ZXM
2. ∆XYM ≅ ∆XZM
3. ∠XYZ = ∠XZY. (Proved)
(ii) Common side.
(iii) XM bisects ∠YXZ.
2. By SAS criterion.
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