Question

1. triangle abc is similar to triangle def. which proportion can be used to find the length of \\(\overline{de}\\) in centimeters? a. \\(\frac{4}{3} = \frac{de}{9}\\) b. \\(\frac{5}{15} = \frac{de}{4}\\) c. \\(\frac{4}{de} = \frac{9}{3}\\) d. \\(\frac{9}{de} = \frac{3}{5}\\)

Explanation:

Step1: Identify Corresponding Sides

In similar triangles \( \triangle ABC \) and \( \triangle DEF \), right angles at \( B \) and \( E \), so \( AB \) corresponds to \( DE \), \( BC \) corresponds to \( EF \), and \( AC \) corresponds to \( DF \). \( AB = 4 \, \text{cm} \), \( BC = 3 \, \text{cm} \), \( EF = 9 \, \text{cm} \), \( DE \) is unknown.

Step2: Set Up Proportion

For similar triangles, the ratio of corresponding sides is equal. So \( \frac{AB}{BC} = \frac{DE}{EF} \). Substituting values: \( \frac{4}{3} = \frac{DE}{9} \), which matches option A.

Answer:

A. \( \frac{4}{3} = \frac{DE}{9} \)