We can easily construct an equilateral triangle with a pair of compasses. Start by drawing a line AB.

Open the compass to the same length as AB and put the compass needle at B. Draw an arc as shown.

Now put the compass needle at A and draw another arc that crosses the first arc as shown.

The point where the arcs cross is the third vertex of an equilateral triangle, after A and B. Join up the vertices.

Each angle in the triangle is 60 Degrees.