1. Cut your piece of paper along one of its diagonals to form two congruent right triangles.[br]2. In each right triangle, draw an altitude from the right angle vertex to the hypotenuse.[br]3. Label each triangle as shown in the following diagram. Flip each one over and label with the same names on the back as on the front. Label the altitude d on both sides, and the hypotenuse of the big triangle is c (I forgot those...).[br]4. Cut one of the triangles along the altitude to form two smaller right triangles.[br]5. Arrange the three triangles in a way that convinces you that all three right triangles are similar. Write a similarity statement involving all three triangles below

6. Write at least 5 proportionality statements to represent relationships between the sides of the triangles. Use a,b,c,d,x,y in your proportions, making sure some of your proportions involve x and y.

7. Solve one of your proportions for x and another for y. Manipulate your equations until you can show [math]a^2+b^2=c^2[/math]. Remember that x+y=c

Use your set of triangles to find the values of x and y in the diagram.