Question

Angles X,Y and Z are equal. Prove that triangle XYZ is an equilateral triangle.

Answer 1

Answer:

please check the Explaination and mark me as Brainliest, it took me a lot of time to write all this

Step-by-step explanation:

Here we will prove that if the three angles of a triangle are equal, it is an equilateral triangle.

Given: In ∆XYZ, ∠YXZ = ∠XYZ = ∠XZY.

Statement

1. XY = ZX.

2. XY = YZ.

3. XY = YZ = ZX.

(Proved)

Reason

1. Sides opposite to equal angles ∠XZY and ∠XYZ.

2. Sides opposite to equal angles ∠XZY and ∠ZXY.

3. from statement 1 and 2.

Note: In the adjoining figure, ∆XYZ is an isosceles triangle in which XY = XZ. XM is the bisector of ∠YXZ

If the triangle is folded along the line XM, the side XY will fall along XZ because ∠YXM = ∠ZXM, and Y will coincide with Z as XY = XZ. Thus, YM will coincide with ZM. This shows ∠XYZ = ∠XZY.

Also, ∠XMY = ∠XMZ = 90°. ∆XYM coincides with ∆XZM. So, ∆XYZ is said to be symmetrical about the line XM. The line XM is called the axis of symmetry.An isosceles triangle has one axis of symmetry while the equilateral ∆ABC has three axes of symmetry, AP, BQ and CR.