Question

determine whether triangles abc and dbe are similar by following these steps. ab/db = 3 ✔️ 4. find and simplify this ratio: cb/eb = 4 ✔️ 5. are the corresponding side lengths proportional? no ✔️ 6. what can you conclude based on your answer to the previous question? the triangles are dropdown with congruent, similar, not similar check

Explanation:

Step1: Calculate AB and DB lengths

From the diagram, \( AB = AD + DB = 10.4 + 5.2 = 15.6 \), \( DB = 5.2 \). So \( \frac{AB}{DB}=\frac{15.6}{5.2}=3 \).

Step2: Calculate CB and EB lengths

\( CB = CE + EB = 23.4 + 7.8 = 31.2 \), \( EB = 7.8 \). So \( \frac{CB}{EB}=\frac{31.2}{7.8}=4 \).

Step3: Check proportionality

For similarity, the ratios of corresponding sides should be equal. Here \( \frac{AB}{DB}=3 \) and \( \frac{CB}{EB}=4 \), which are not equal. Also, we should check the included angle (∠B is common). But since the side ratios are not equal, the triangles don't satisfy the SAS similarity criterion.

Step4: Conclude similarity

Since the corresponding side lengths are not proportional (ratios are different), the triangles are not similar.

Answer:

not similar