Question

show that in an isosceles triangle, angles opposite to equal sides are equal​

Answer 1

Step-by-step explanation:

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. Given: In the isosceles ∆XYZ, XY = XZ. ... Construction: Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.

Answer 2

Step-by-step explanation:

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.