Question

determine whether triangles abc and dbe are similar by following these steps. 1. ∠abc is congruent to ∠dbe. 2. to use sas similarity, ab and cb must be proportional to db and eb, respectively. 3. find and simplify this ratio: ab/db = check

Explanation:

Step1: Find lengths of AB and DB

From the diagram, \( AB = AD + DB \). Given \( AD = 10.4 \) and \( DB = 5.2 \), so \( AB = 10.4 + 5.2 = 15.6 \). And \( DB = 5.2 \).

Step2: Calculate the ratio \( \frac{AB}{DB} \)

Substitute the values of \( AB \) and \( DB \) into the ratio: \( \frac{AB}{DB}=\frac{15.6}{5.2} \). Simplify this fraction by dividing numerator and denominator by \( 5.2 \): \( \frac{15.6\div5.2}{5.2\div5.2}=\frac{3}{1} = 3 \).

Answer:

\( 3 \)