Complete the proof of the Pythagorean theorem. Given: is a right triangle, with
a right angle at .

Prove:

triangle
A right triangle B C A. Angle C is marked as a right triangle. Side B C is labeled as a. Side C A is labeled as b. A line segment drawn from vertex C intersects the line segment B A at a point labeled as D. Segment B D is labeled as x. Segment D A is labeled as y. Angle C D A is marked as a right angle. A line segment that runs parallel to segment BA is labeled as c.