One Into Three

Strategies and Hints

  1. As stated in the problem, the length of segment AE equals half the length of the diagonal of the square.

  2. Segment AF must be perpendicular to segment DE. To find point F, draw a line through point A so that it intersects segment DE to form a right angle. In the same way, draw a line through point C so that it intersects segment DE to form a right angle. This gives the location of point G.

  3. The distance from point K to point is G equal to the length of segment AF. Likewise, point L is that same distance from point F.

  4. The small square is made from pieces 3 and 4.

Solution