1. **State the problem:** We have two right triangles, one larger with legs 16 and 16, and a smaller one with legs 9 and 9. We need to find the scale factor from the larger triangle to the smaller triangle. 2. **Formula and concept:** The scale factor between two similar triangles is the ratio of corresponding sides. Since both triangles are right triangles and the smaller is a scaled copy, the scale factor $k$ is given by: $$k = \frac{\text{side of smaller triangle}}{\text{corresponding side of larger triangle}}$$ 3. **Calculate the scale factor:** Using the legs: $$k = \frac{9}{16}$$ 4. **Simplify the fraction:** The fraction $\frac{9}{16}$ is already in simplest form because 9 and 16 have no common factors other than 1. 5. **Final answer:** The scale factor from the larger triangle to the smaller triangle is: $$\boxed{\frac{9}{16}}$$