Construct an equilateral triangle

Construct an equilateral triangle with one vertex on each of three parallel lines using just a straight edge and a pair of compasses. construct-an-equilateral-triangle-figure-1

Reveal Solution

Add a point on the middle line and use a compass with a fixed width to create a line at 60° to the parallel lines at this point.

construct-an-equilateral-triangle-figure-2 Construct a line parallel to this with the same distance between them as the bottom two lines: find the point of intersection of this line with the bottom line, construct a circle through this point with centre on the original point, find the intersections of this circle with the bottom two lines and draw a line through these.

construct-an-equilateral-triangle-figure-3 Find the intersection of this line with the top line and then draw a circle with a centre on the original point that passes through this point. Find the intersection of this circle with the bottom line (on the same side as the top point).