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
ABC is an equilateral triangle.
AB = BC = CA
∠1= ∠2= ∠3
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
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
∠1 = ∠2 = ∠3 = 60 degree
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