Question

Prove that the angles opposite to equal sides of an irosceles triangle are equal.​

Answer 1

Answer:

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. (Given.)

(ii) XM = XM. (Common side.)

(iii) ∠YXM = ∠ZXM. ( XM bisects ∠YXZ.)

2. ∆XYM ≅ ∆XZM. (By SAS criterion.)

By CPCTC.

3. ∠XYZ = ∠XZY. (Proved)

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