Question

1. a triangular billboard frame has two sides measuring 10 meters and 12 meters, with the included angle measuring 60°. another frame has sides of 8 meters and 9 meters with the same 60° included angle. are the triangular frames similar? a. yes, by the sas criterion b. no, the sides are not proportional c. yes, by the sss criterion d. no, the angles do not match

Explanation:

Step1: Recall similarity criterion

The Side - Angle - Side (SAS) similarity criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Step2: Check side - side ratio

For the first triangle with sides \(a_1 = 10\), \(b_1=12\) and the second triangle with sides \(a_2 = 8\), \(b_2 = 9\). Calculate the ratios \(\frac{a_1}{a_2}=\frac{10}{8}=\frac{5}{4}\) and \(\frac{b_1}{b_2}=\frac{12}{9}=\frac{4}{3}\). Since \(\frac{5}{4}
eq\frac{4}{3}\), the sides are not proportional.

Answer:

B. No, the sides are not proportional