STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 0

0. Draw an equilateral triangle.

Solution

1. Draw a line, A.
2. Mark two arbitrary points on A, b and c, not coincident. ( The distance bc will be the length of each side of the triangle.)
3. Draw a circle, centre b, radius bc. ( This is two steps rolled into one: 1. Set the compasses to radius bc 2. Draw a circle centred on b )
4. Draw a circle, centre c, radius bc.
5. The two circles will intersect in two points, d and d', one either side of A.
6. Draw the line segments bd and cd. bcd is the equilateral triangle. ( Since lengths bd = bc = cd )