# Angles Opposite to Equal Sides of an Isosceles Triangle are Equal

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:

 Statement1. In ∆XYM and ∆XZM,(i) XY = XZ(ii) XM = XM(iii) ∠YXM = ∠ZXM2. ∆XYM ≅ ∆XZM 3. ∠XYZ = ∠XZY. (Proved) Reason1.(i) Given.(ii) Common side.(iii) XM bisects ∠YXZ.2. By SAS criterion. 3. CPCTC.

9th Grade Math

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