Question

8.
scale factor= ______
missing side length =______

Explanation:

Step1: Determine Scale Factor

The triangles are similar (AA similarity, as two angles are equal). The corresponding sides are \( BC = 9 \) and \( EF = 6 \). The scale factor from \( \triangle ABC \) to \( \triangle DEF \) is \( \frac{EF}{BC}=\frac{6}{9}=\frac{2}{3} \).

Step2: Find Missing Side Length

The side \( AC = 15 \) in \( \triangle ABC \) corresponds to \( DF = x \) in \( \triangle DEF \). Using the scale factor \( \frac{2}{3} \), we have \( x = AC\times\frac{2}{3}=15\times\frac{2}{3} \).
\( 15\times\frac{2}{3}=10 \).

Answer:

Scale Factor = \(\frac{2}{3}\)
Missing Side length = \(10\)