# In triangle RST, RS = 10, RT = 15, and angle R = 32. In triangle UVW, UV=12, UW = 18, and angle U = 32. Are these polygons similar?

Sep 25, 2016

The corresponding sides are in the same ratio.
The triangles are similar.

#### Explanation:

Draw a sketch of the two triangles and fill in the given values.
We have been given the lengths of corresponding sides.
The combination is "two sides and the included angle in each case.

Are the given sides in the same ratio?

$\frac{10}{12} \mathmr{and} \frac{15}{18} \text{ } \leftarrow$ simplify each

$\frac{5}{6} \mathmr{and} \frac{5}{6} \text{ } \leftarrow$ the ratios are equal

OR

$\frac{10}{15} \mathmr{and} \frac{12}{18}$

$\frac{2}{3} \mathmr{and} \frac{2}{3} \text{ } \leftarrow$ the ratios are equal