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