Question

a flagpole casts a shadow 24 meters long, and a nearby pole 3 meters tall casts a shadow 4 meters long. which criterion confirms the similarity of the triangles? a. sss criterion b. aa criterion c. right triangle criterion d. sas criterion 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. no, the sides are not proportional b. no, the angles do not match c. yes, by the sss criterion d. yes, by the aa criterion

Explanation:

Step1: Analyze first question

The flag - pole and the nearby pole form right - angled triangles with the ground and their shadows. The angles of elevation of the sun are the same for both, and both have a right - angle (pole and ground). So we use AA (angle - angle) criterion for similarity.

Step2: Analyze second question

For the two triangular signs, check the ratio of corresponding sides. $\frac{9}{15}=\frac{3}{5}$, $\frac{12}{20}=\frac{3}{5}$, $\frac{15}{25}=\frac{3}{5}$. Since the ratios of all corresponding sides are equal, by the SSS (side - side - side) criterion, the triangles are similar.

Answer:

1. b. AA Criterion
2. c. Yes, by the SSS Criterion