Question

1. in △rst, rs = 10, rt = 15, and m∠r = 32. in △uvw, uv = 12, uw = 18, and m∠u = 32. are the polygons similar? if they are, write a similarity statement and give the similarity ratio.

△rst ~ △vwu; 5:6
the triangles are not similar.
△rst ~ △vwu; 6:5
△rst ~ △uvw; 5:6

Explanation:

Step1: Calculate side - length ratios

For two triangles $\triangle{RST}$ and $\triangle{UVW}$, we check the ratios of corresponding sides. Let's assume $RS$ corresponds to $UV$, $RT$ corresponds to $UW$. The ratio of the first pair of corresponding sides is $\frac{RS}{UV}=\frac{10}{12}=\frac{5}{6}$, and the ratio of the second pair of corresponding sides is $\frac{RT}{UW}=\frac{15}{18}=\frac{5}{6}$. But we don't know if the included angles are equal. Since we only have two - side ratios and no information about the included angles, we cannot conclude similarity.

Answer:

The triangles are not similar.