Question

quiz 2: similar polygons
if $\triangle abc \sim \triangle xyz$, the side lengths of $\triangle abc$ are 8, 5, and 2 respectively, and the side lengths of $\triangle xyz$ are 32, 20, and 8 respectively, then the scale factor is:

1. $\frac{1}{4}$
2. none of the choices are correct.

Explanation:

Step1: Identify corresponding sides

For similar triangles \( \triangle ABC \) and \( \triangle XYZ \), we need to find the ratio of corresponding sides. Let's pair the sides: \( 8 \) (from \( \triangle ABC \)) with \( 32 \) (from \( \triangle XYZ \)), \( 5 \) with \( 20 \), and \( 2 \) with \( 8 \).

Step2: Calculate the ratio

Calculate the ratio of a side from \( \triangle ABC \) to the corresponding side from \( \triangle XYZ \). Let's take the first pair: \( \frac{8}{32} = \frac{1}{4} \), or the second pair: \( \frac{5}{20} = \frac{1}{4} \), or the third pair: \( \frac{2}{8} = \frac{1}{4} \). So the scale factor from \( \triangle ABC \) to \( \triangle XYZ \) is \( \frac{1}{4} \).

Answer:

\(\frac{1}{4}\)