                 Quick Answer: Draw segments XZ and YZ with equal lengths as in the picture. The three pieces can be formed into a square as shown: Any two squares can be used to make a third square in this manner. Complete Solution: The Hint and the Answer suggest using a piece of paper to find point Z and construct a square. (The edges of the paper will lie on two sides of the new square. Carpenters would use a carpenter’s square for finding this point.) A different way to find point Z is to mark off the length of a side of the small square along the bottom of the larger square starting at the left. This length locates point Z. Because the total length of the bottom is the sum of the lengths of a side of each square, Z also separates the bottom into two lengths that are the lengths of the sides of the squares. Draw segments XZ and YZ. The two right triangles are the same size and shape because each has a right angle and the two smaller sides are each a length of the original squares. Because the triangles are the same size and shape, XZ and YZ are the same length. They become sides of the new square. Using the angles of the triangles along the base, angle XZY can be shown to be a right angle.      Home · Back to the Challenge · Try These · Think About This  ·  Did You Know? · Resources Try Another Challenge · Challenge Index · Math Index · Printing the Challenges · En Español Family Corner · Teacher Corner · About Figure This! · Purchase the CD  ©2004 National Council of Teachers of Mathematics Web site and CD-ROM design/production © 1999-2004 KnowNet Construction, Inc.    