1. **State the problem:** We are given two triangles with sides labeled and asked which proportion could NOT be used to solve for $x$ given the sides: $$\frac{x}{5} = \frac{35}{9}$$ 2. **Recall the rule for proportions in similar triangles:** Corresponding sides of similar triangles are proportional. This means the ratio of one side in the first triangle to the corresponding side in the second triangle equals the ratio of another pair of corresponding sides. 3. **Check each proportion:** - First proportion: $$\frac{x}{5} = \frac{35}{9}$$ This matches the ratio of $x$ to 5 and 35 to 9, consistent with corresponding sides. - Second proportion: $$\frac{x}{9} = \frac{35}{5}$$ This swaps the denominators and numerators incorrectly, mixing corresponding sides. - Third proportion: $$\frac{35}{x} = \frac{5}{9}$$ This flips the ratio on the left side, which is not consistent with the original setup. 4. **Conclusion:** The proportion that could NOT be used is the second one: $$\frac{x}{9} = \frac{35}{5}$$ because it mismatches corresponding sides and does not represent the correct ratio for similar triangles. **Final answer:** The proportion $$\frac{x}{9} = \frac{35}{5}$$ could NOT be used to solve the problem.