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.


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.



1. In ∆XYM and ∆XZM,

(i) XY = XZ

(ii) XM = XM

(iii) ∠YXM = ∠ZXM

2. ∆XYM ≅ ∆XZM

3. ∠XYZ = ∠XZY. (Proved)



(i) Given.

(ii) Common side.

(iii) XM bisects ∠YXZ.

2. By SAS criterion.


9th Grade Math

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