Question

the two polygons below are similar.complete the similarity statement.stuv ~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: Identify corresponding angles

Since the polygons are similar, we match the angles. In \(STUV\), angle \(T\) corresponds to angle \(I\), angle \(S\) corresponds to angle \(J\), angle \(V\) corresponds to angle \(K\), and angle \(U\) corresponds to angle \(H\).

Step2: Write the similarity statement

The order of the letters in the similarity statement must follow the correspondence of angles. So \(STUV\sim IJKH\)

Step3: Find the ratio of side - lengths

Take a pair of corresponding sides. For example, side \(ST = 1\) and its corresponding side \(IJ=3\). The ratio of a side length in the first polygon (\(STUV\)) to its corresponding side length in the second polygon (\(IJKH\)) is \(\frac{ST}{IJ}=\frac{1}{3}\)

Answer:

1. \(STUV\sim IJKH\)
2. \(\frac{1}{3}\)