Question

1. a triangular roof truss has side lengths of 9 feet, 12 feet, and 15 feet. another roof truss is designed with side lengths of 6 feet, 9 feet, and 10 feet. are the two trusses similar? a. yes, by the sas criterion b. no, the angles do not match c. no, the sides are not proportional d. yes, by the sss criterion

Explanation:

Step1: Recall similarity criterion

For two triangles to be similar, the ratios of their corresponding sides must be equal.

Step2: Calculate side - length ratios

For the first truss with side lengths 9, 12, 15 and the second truss with side lengths 6, 9, 10. Calculate the ratios: $\frac{9}{6}=\frac{3}{2}$, $\frac{12}{9}=\frac{4}{3}$, $\frac{15}{10}=\frac{3}{2}$. Since $\frac{3}{2}
eq\frac{4}{3}$, the sides are not proportional.

Answer:

c. No, the sides are not proportional