Triangle Similarity Theorems and Pythagorean Theorem Practice Test

In the diagram, $\triangle ABC$ is a right triangle with right angle at $C$. Segment $CD$ is drawn from $C$ to the hypotenuse $AB$, and $CD \perp AB$ at $D$. The legs are labeled $AC=b$ and $BC=a$, and the hypotenuse is labeled $AB=c$. Using triangle similarity created by the altitude (not memorization of a formula), which conclusion can be proven using the diagram?

In the diagram, $\triangle ABC$ is right at $C$, and altitude $CD$ is drawn to hypotenuse $AB$ with $CD \perp AB$. Let $AD=x$, $DB=y$, and $AB=c$. Which proportion leads to the Pythagorean relationship by combining results from the similar triangles?