Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.

Let ABC be a right triangle. Construct an altitude from the right angle to the opposite side. Label the point of intersection with this side point D. Name segment AC, b: segment CB, a: segment AB, c: segment AD, x; and segment DB, y. c/a=a/y and c/b=b/x	By the ______ _____ _____ _____ _____ Theorem.
b^2 = cx and a^2 = cy	2. _____ _____ Property
a^2+b^2 = cy+b^2	3.
a^2+b^2 = cy+cx	4.
a^2+b^2 = c(y+x)	5.
y+x=c. Substitute this expression into the original equation to result in a^2+b^2 = c(c). Simplify: a^2 + b^2 = c^2	6. Give a reason for why y+x=c