Construction Protocol for an Equilateral Triangle

To construct an equilateral triangle with a given line segment as its side.
Discuss the following: 1. Why does this construction work? 2. Is it better to define an equilateral triangle as a triangle having equal sides or equal angles? 3. Notice how we get an inverted equilateral triangle for free. Why does this happen? 4. You just constructed a rhombus! Do you see it?