Subscribe to our YouTube channel for the latest videos, updates, and tips.


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.

Proof:

   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.

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




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.



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.




Share this page: What’s this?

Recent Articles

  1. Speed Distance and Time | Relation between Speed Distance and Time

    May 21, 25 12:58 PM

    Speed is defined as the distance covered per unit time. Speed = (Distance Travelled)/(Time Taken) Or, S = D/T. Speed also requires a unit of measurement. If the distance is in kilometres

    Read More

  2. Math Problem Answers | Solved Math Questions and Answers | Free Math

    May 21, 25 12:45 PM

    Partial fraction
    Math problem answers are solved here step-by-step to keep the explanation clear to the students. In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades

    Read More

  3. Test of Divisibility | Divisibility Rules| Divisible by 2, 3, 5, 9, 10

    May 21, 25 10:29 AM

    The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not. Test of divisibility by 2: A number is divisible by 2

    Read More

  4. Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

    May 21, 25 10:17 AM

    Divisible by 7
    Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

    Read More

  5. Average Word Problems | Worksheet on Average Questions with Answers

    May 20, 25 05:40 PM

    In average word problems we will solve different types of problems on basic concept of average. 1. Richard scored 80, 53, 19, 77, 29 and 96 runs in 6 innings in a series. Find the average runs scored…

    Read More