Question

What are the steps for using a compass and straightedge to construct an equilateral triangle?

Answer 1

The steps for using a compass and straightedge to construct an equilateral triangle are as follows:

1. Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF

2. Construct line ​ EF

3. Construct a point at one of the two intersection points of circle E and circle F and label this point G

4. Construct line​ EG and line​ FG.

Answer 2

Let's take a look at the available steps and see what makes sense. "Construct a point at one of the two intersection points of circle E and circle F and label this point G" ** We don't have anything drawn yet, so this step goes later. "Construct EG¯¯¯¯¯ ​ and FG¯¯¯¯¯​" ** Same issue, nothing done yet. But this looks like it would be the last step. "Construct ​ EF¯¯¯¯¯​" ** OK. We can draw a line and label the end points E and F. So make this step 1. "Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF" ** This looks like it would also work for step 2, since we've already constructed the line segment EF. So the entire process looks like: 1. Construct ​ EF¯¯¯¯¯​ 2. Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF . 3. Construct a point at one of the two intersection points of circle E and circle F and label this point G. 4. Construct EG¯¯¯¯¯ ​ and FG¯¯¯¯¯​.