Question

use the image to answer the question.
△abc is similar to △def. find the ratio between △def and △abc. express the answer as a fraction in simplest form.
(1 point)

Explanation:

Step1: Identify corresponding sides

First, we need to find the corresponding sides of the similar triangles \( \triangle ABC \) and \( \triangle DEF \). By looking at the angles, we can match the sides. Let's list the sides:

For \( \triangle ABC \): \( AC = 16 \), \( BC = 24 \), \( AB = 22 \)

For \( \triangle DEF \): \( DF = 8 \), \( EF = 12 \), \( DE = 11 \)

We can check the ratios of corresponding sides. Let's take \( AC \) and \( DF \), \( BC \) and \( EF \), \( AB \) and \( DE \).

Step2: Calculate the ratio of corresponding sides

Let's calculate the ratio of \( DF \) to \( AC \): \( \frac{DF}{AC} = \frac{8}{16} = \frac{1}{2} \)

Ratio of \( EF \) to \( BC \): \( \frac{EF}{BC} = \frac{12}{24} = \frac{1}{2} \)

Ratio of \( DE \) to \( AB \): \( \frac{DE}{AB} = \frac{11}{22} = \frac{1}{2} \)

Since the triangles are similar, the ratio of \( \triangle DEF \) to \( \triangle ABC \) is the ratio of their corresponding sides, which is \( \frac{1}{2} \).

Answer:

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