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

Explanation:

Step1: Check ratio of corresponding sides

For $\triangle{RST}$ and $\triangle{UVW}$, we find the ratio of corresponding sides. $\frac{RS}{UV}=\frac{10}{12}=\frac{5}{6}$, $\frac{RT}{UW}=\frac{15}{18}=\frac{5}{6}$.

Step2: Check angle - equality

We are given $\angle{R} = 32^{\circ}$ and $\angle{U}=32^{\circ}$, so $\angle{R}\cong\angle{U}$.

Step3: Determine similarity

Since the ratios of corresponding sides are equal and one pair of corresponding angles are equal, the triangles are similar. The similarity statement is $\triangle{RST}\sim\triangle{UVW}$ and the similarity ratio is $\frac{5}{6}$.

Answer:

$\triangle{RST}\sim\triangle{UVW};\frac{5}{6}$