# Equilateral triangles have equal angles

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

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