Question

construct an argument determine whether the following statement is sometimes, always, or never true. equilateral triangles are congruent. the statement is select choice true because equilateral triangles select choice have corresponding sides congruent

Explanation:

Step1: Recall congruence and equilateral triangles

Congruent triangles have all corresponding sides and angles equal. An equilateral triangle has all sides equal (each angle is \(60^\circ\)), but the side lengths can vary. For example, one equilateral triangle can have side length \(3\) and another can have side length \(5\). These two would not be congruent because their corresponding sides are not equal (even though all their angles are \(60^\circ\)). However, if two equilateral triangles have the same side length, they are congruent. So equilateral triangles are congruent only when their side lengths are equal, which means the statement "Equilateral triangles are congruent" is sometimes true because equilateral triangles sometimes have corresponding sides congruent (when their side lengths match) and sometimes do not (when side lengths differ).

Step2: Fill in the blanks

The first "Select Choice" should be "sometimes" because the congruence of equilateral triangles depends on their side lengths (they are congruent only when side lengths are equal, not always). The second "Select Choice" should be "sometimes" because equilateral triangles sometimes (when side lengths are equal) have corresponding sides congruent, and sometimes (when side lengths differ) do not.

Answer:

The first dropdown: sometimes; The second dropdown: sometimes