Question

what is the scale factor from δdef to δabc?
scale factor: ________
the right triangle on the left. identify

Explanation:

Step1: Identify corresponding sides

First, we need to find the corresponding sides of the two similar triangles \( \triangle DEF \) and \( \triangle ABC \). By looking at the angles (the marked angles are equal, so the triangles are similar), we can match the sides:

• \( DE = 20 \) corresponds to \( AB = 10 \)
• \( EF = 12 \) corresponds to \( BC = 6 \)
• \( DF = 14 \) corresponds to \( AC = 7 \)

Step2: Calculate the scale factor

The scale factor from \( \triangle DEF \) to \( \triangle ABC \) is the ratio of the length of a side in \( \triangle ABC \) to the corresponding side in \( \triangle DEF \). Let's take one pair of corresponding sides, say \( AB \) and \( DE \). The scale factor \( k \) is given by:
\( k=\frac{AB}{DE}=\frac{10}{20}=\frac{1}{2} \)
We can check with another pair, like \( BC \) and \( EF \): \( \frac{BC}{EF}=\frac{6}{12}=\frac{1}{2} \), or \( AC \) and \( DF \): \( \frac{AC}{DF}=\frac{7}{14}=\frac{1}{2} \). All ratios are the same, so the scale factor is consistent.

Answer:

\( \frac{1}{2} \)