Three Angles of an Equilateral Triangle are Equal 

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.

Three Angles of an Equilateral Triangle

To prove: XY = YZ = ZX.



1. XY = ZX.

2. XY = YZ.

3. XY = YZ = ZX.



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.

Bisector of an Isosceles Triangle

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.

Three Axes of Symmetry of an Equilateral Triangle

An isosceles triangle has one axis of symmetry while the equilateral ∆ABC has three axes of symmetry, AP, BQ and CR.

9th Grade Math

From Three Angles of an Equilateral Triangle are Equal to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More