Question

2 are the triangles similar? explain. downloaded by r. brown. this resource expires on 6/30/2024. lesson 7 describe angle relationships in triangles 141

Explanation:

Step1: Check ratio of corresponding sides

For the sides of the two triangles, find the ratios. Let the first - triangle have side lengths \(a_1 = 8\), \(b_1 = 12\), \(c_1 = 16\) and the second - triangle have side lengths \(a_2 = 10\), \(b_2 = 15\), \(c_2 = 20\). Calculate the ratios \(\frac{a_1}{a_2}=\frac{8}{10}=\frac{4}{5}\), \(\frac{b_1}{b_2}=\frac{12}{15}=\frac{4}{5}\), \(\frac{c_1}{c_2}=\frac{16}{20}=\frac{4}{5}\).

Step2: Apply similarity criterion

Since the ratios of the corresponding sides of the two triangles are equal (\(\frac{8}{10}=\frac{12}{15}=\frac{16}{20}=\frac{4}{5}\)), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

Yes, the triangles are similar because the ratios of their corresponding sides are equal.