In this chapter we will prove that all angles of equilateral triangles are equal and they measure 60 degrees.

Proving all angles of equilateral triangles are equal

**Given;**

ABC is an equilateral triangle.

AB = BC = CA**To Prove**

∠1= ∠2= ∠3

**Proof**

We know that angle opposite to equal side are equal.

Since AB = AC; we can say that ∠2 = ∠3.

Similarly as AB = BC, we can write ∠1 = ∠3.

Combining the above two expression, we can say that;

∠1 = ∠2 = ∠3

Hence, we proved that in equilateral triangles all interior angles are equal.

## Prove that all angles of equilateral triangle measure 60 degrees

**Given:**

Consider the equilateral triangle ABC in which AB = BC = CA.

We know that all angles of equilateral triangle are equal, we can write;

∠1 = ∠2 = ∠3 = x degree

**To prove:**

∠1 = ∠2 = ∠3 = 60 degree **Solution**

Applying angle sum property of triangle.

We know that **sum of interior angle of triangle equals 180 degree.**

**∠1 + ∠2 + ∠3 = 180**

Since ∠1 = ∠2 = ∠3 = x, the above equation can be written as;

x + x + x = 180

3x = 180

x = 180 / 3

x = 60 degree

Hence, we proved that ∠1 = ∠2 = ∠3 = 60

This means that in equilateral triangle all interior angle measures 60 degrees.

**Next chapter :** **Questions on congruent triangles**