We are given three similar triangles and the proportion $\frac{c}{a} = \frac{a}{?}$. We need to find the letter that completes the proportion based on the similarity of the triangles in the figure.

1. Problem Description

We are given three similar triangles and the proportion $\frac{c}{a} = \frac{a}{?}$. We need to find the letter that completes the proportion based on the similarity of the triangles in the figure.

2. Solution Steps

Let's analyze the triangles. We have three similar right triangles.

The largest triangle has sides $c$, $a+b$, and a side along the altitude that we don't need to name for this problem.

The smallest triangle has sides $a$, $z$, and $y$.

There is a middle-sized triangle with hypotenuse $c$, one leg of length $y+z$, and the other leg of length $x$.

We are given the proportion $\frac{c}{a} = \frac{a}{?}$.

Here, $c$ is the hypotenuse of the larger triangle, and $a$ is one of its legs.

The $a$ in the numerator of the right-hand side is the hypotenuse of the smaller triangle.

Therefore, we need to find the leg in the smaller triangle that corresponds to the leg $a$ in the larger triangle.

In the larger triangle, $a$ is opposite to one of the acute angles. In the smaller triangle, we look for a side opposite the same acute angle. That side is $y$.

Therefore, the correct proportion is $\frac{c}{a} = \frac{a}{y}$.

3. Final Answer

y