Angles Opposite to Equal Sides of an Isosceles Triangle are Equal

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

Solution:

Angles Opposite to Equal Sides of an Isosceles Triangle 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.

Proof:

          Statement

1. In ∆XYM
and ∆XZM,

(i) XY = XZ

(ii) XM = XM

(iii) ∠YXM =
∠ZXM

2. ∆XYM ≅ ∆XZM

3. ∠XYZ =
∠XZY. (Proved)

          Reason

1.

(i) Given.

(ii) Common side.

(iii) XM bisects ∠YXZ.

2. By SAS criterion.

3. CPCTC.

9th Grade Math

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