Chapter 4.3, Problem 43HP

To determine

To identify:

Given statement are sometimes, always or never true.

Answer to Problem 43HP

Given statement “Equilateral triangles are congruent.” is sometimes true.

Explanation of Solution

Given information:

Given statement: Equilateral triangles are congruent.

Calculations:

Each angle of an equilateral triangle is measure of $60$ . Thus two equilateral triangles are always with three pairs of corresponding congruent angles.

In case two equilateral triangles are with same side length, then two equilateral triangles are three pairs of congruent sides. In this case, the two equilateral triangles are congruent.

In case two equilateral triangles are with different side lengths, then the two equilateral triangles are not with congruent sides. In this case, two equilateral triangles are not congruent.

Hence, the answer is sometimes which is equilateral triangles are sometimes congruent.