1. The problem asks to write three proportions involving the geometric mean from the similar right triangles $\triangle GIF$ and $\triangle GHF$. 2. In right triangle similarity with an altitude to the hypotenuse, the geometric mean relationships are: $$\frac{a}{w} = \frac{w}{y} = \frac{a}{x} = \frac{x}{z} = \frac{y}{h} = \frac{h}{z}$$ 3. These proportions come from the fact that the altitude $h$ creates two smaller right triangles similar to the original, and the segments $y$ and $z$ on the hypotenuse satisfy these geometric mean relations. 4. Checking the options, option D matches these proportions: $$a/w = w/y, \quad a/x = x/z, \quad y/h = h/z$$ 5. Therefore, the correct answer is option D. Final answer: D. $a/w = w/y$, $a/x = x/z$, $y/h = h/z$