Sides Opposite to the Equal Angles of a Triangle are Equal

Here we will prove that the sides opposite to the equal angles of a triangle are equal.

Given: In ∆ABC, ∠XYZ = ∠XZY.

Sides Opposite to the Equal Angles of a Triangle are Equal

To prove: XY = XZ.

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.

Proof:

          Statement

1. In ∆XYM and ∆XZM,

(i) ∠XYM = XZM

(ii) ∠YXM = ∠ZXM

(iii) XM = XM.


2. ∆XYM ≅ ∆XZM

3. XY = XZ. (Proved)

          Reason

1.

(i) Given.

(ii) XM bisects ∠YXZ.

(iii) Common side.


2. By AAS criterion.

3. CPCTC.



9th Grade Math

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