Question

1. a triangular sign has sides measuring 15 feet, 20 feet, and 25 feet. another sign has sides measuring 9 feet, 12 feet, and 15 feet. are the triangular signs similar? a. yes, by the aa criterion b. no, the angles do not match c. yes, by the sss criterion d. no, the sides are not proportional

Explanation:

Step1: Check side - length ratios

For the first triangle with side - lengths \(a_1 = 15\), \(b_1 = 20\), \(c_1 = 25\) and the second triangle with side - lengths \(a_2=9\), \(b_2 = 12\), \(c_2 = 15\). Calculate the ratios: \(\frac{a_1}{a_2}=\frac{15}{9}=\frac{5}{3}\), \(\frac{b_1}{b_2}=\frac{20}{12}=\frac{5}{3}\), \(\frac{c_1}{c_2}=\frac{25}{15}=\frac{5}{3}\).

Step2: Apply similarity criterion

Since the ratios of the corresponding sides of the two triangles are equal (\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

c. Yes, by the SSS Criterion