Question

An equilateral triangle has three sides with equal length and three angles with equal measure. Given equilateral triangles, ∆ ABC and ∆ DEF complete the statements below.

1. ∆ABC ≅ ∆ DEF______________
2. If <B ≅ <E and m<B = 60° then m<E_________°
3. ∆ABC ~ ∆DEF______________

Answer 1

1. ∆ABC ≅ ∆DEF — Not necessarily. (Being equilateral makes their shapes the same, but not necessarily the same size; congruence needs corresponding side lengths equal.)

2. m∠E = 60°

3. ∆ABC ~ ∆DEF — Yes, by AAA (all angles are 60°), so the triangles are similar.