Question

Are all equilateral triangles congruent Yes No?

Answer 1

Answer: No

Reasoning:

Equilateral triangles can have differing side lengths, but they all have congruent angles (60°). Therefore, all equilateral triangles are similar, but not always congruent.

Let’s see why the angles always measure 60°:

Given an equilateral triangle with three sides: a, a, a. Find the angle measure of the interior angles, denoted as x.

We know by the Triangle Sum Theorem, that all interior angles of a triangle sum up to 180.° Because the triangle is an equilateral triangle, all angle measures of x will be equal, so we can create an equation:

x+x+x=180

3x=180

x=180/3

x=60°

Answer 2

All equilateral triangles are NOT congruent.

Only those equilateral triangles whose sides have the same length will be congruent.

Those whose sides have different lengths will not be congruent.

By the criteria of congruence:

• Side Angle Side: Two triangles are congruent if two sides of one triangle have the same measure as the two sides of the other, the angle being equilateral if they have the same (60º)
• Side Side Side: Two triangles are congruent if all three sides of one have the same length as the other.
• Angle Side Angle: Two triangles are congruent if two of their angles and the side between the two angles are equal in the other triangle.