Question

Are all equilateral triangles similar?

Answer 1

In an equilateral triangle, all the lengths of the sides are equal.

In such a case, each of the interior angles will have a measure of$60°$

Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle.

A property of equilateral triangles includes that all of their angles are equal to $60°$

The $AAA$Triangle Similarity Postulate asserts that if all of the angles in a triangle are equal to the corresponding angles in another triangle, then those two triangles are equal.

Since every equilateral triangle’s angles are$60°$, every equilateral triangle is similar to one another due to this $AAA$Postulate.

Hence, all equilateral triangles are similar.