1. **State the problem:** We have a right triangle with base $a$ and hypotenuse 18. A segment from the right angle perpendicular to the hypotenuse divides it into two parts, the larger part being 16. 2. **Identify the proportion to find $a$:** The problem asks which proportion can be used to find $a$. 3. **Recall the geometric mean theorem:** The altitude to the hypotenuse in a right triangle creates two smaller right triangles similar to the original. The segments of the hypotenuse satisfy the relation $a^2 = (larger\ segment) \times (smaller\ segment)$. 4. **Apply the theorem:** Given the larger segment is 16 and the hypotenuse is 18, the smaller segment is $18 - 16 = 2$. 5. **Write the proportion:** Using the theorem, $a^2 = 16 \times 2$. 6. **Check the options:** Option B is $a^2 = 16a$, which is incorrect because the right side should be $16 \times 2$, not $16a$. Option C is $a18 = 2a$, which is incorrect. Option D is $18a = a16$, which is incorrect. Option A is $34a = a16$, which is incorrect. 7. **Correct proportion:** The correct proportion is $a^2 = 16 \times 2$. **Final answer:** The proportion to find $a$ is $$a^2 = 16 \times 2$$.