Question

Show that the sides opposite to equal angles in a triangle
equal.​

Answer 1

Answer:

Here we will prove that the 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.

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

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

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

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM(ii) ∠YXM = ∠ZXM

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM(ii) ∠YXM = ∠ZXM(iii) XM = XM.

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM(ii) ∠YXM = ∠ZXM(iii) XM = XM.2. ∆XYM ≅ ∆XZM

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.Proof: Statement1. In ∆XYM and ∆XZM,(i) ∠XYM = XZM(ii) ∠YXM = ∠ZXM(iii) XM = XM.2. ∆XYM ≅ ∆XZM3. XY = XZ. (Proved)

Answer 2

Answer:

See the picture for answer.

Step-by-step explanation:

Sides opposite to equal angles of a triangle are equal. Each angle of an equilateral triangle is of 60°. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).

Hope it will help you!!!