Question

the two polygons below are similar.
complete the similarity statement.
rstu ~
find the ratio of a side length in the first polygon to its corresponding side length in the second polygon.
simplify your answer and write it as a proper fraction, improper fraction, or whole number.

Explanation:

Step1: Match corresponding angles

Identify congruent marked angles: $\angle S = 46^\circ$ corresponds to $\angle I = 46^\circ$, $\angle R$ corresponds to $\angle F$, $\angle T$ corresponds to $\angle H$, $\angle U$ corresponds to $\angle G$. So the similarity statement maps vertices in order: $R \to F$, $S \to I$, $T \to H$, $U \to G$.

Step2: Calculate side length ratio

Take corresponding sides: first polygon side = 18, second polygon side = 30. Simplify the ratio $\frac{18}{30}$.
$\frac{18}{30} = \frac{18\div6}{30\div6} = \frac{3}{5}$

Answer:

Similarity statement: $RSTU \sim FIHG$
Ratio of side lengths: $\frac{3}{5}$