Question

2 a triangular sculpture has two sides measuring 14 feet and 18 feet with an included angle of 45°. another triangular sculpture has two sides measuring 7 feet and 10 feet, also with an included angle of 45°. are the sculptures similar? a. no, the sides are not proportional b. yes, by the sas criterion c. yes, by the sss criterion d. no, the angles are not congruent

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 14 and 18, and the second triangle with sides 7 and 10. Calculate the ratios of corresponding sides: $\frac{14}{7}=2$ and $\frac{18}{10} = 1.8$. Since $\frac{14}{7}
eq\frac{18}{10}$, the sides are not proportional.

Answer:

a. No, the sides are not proportional