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 dropdown db and eb, resp options: greater than, less than, proportional to

diagram: triangle abc with point d on ab, point e on cb. lengths: ad = 10.4, db = 5.2, ce = 23.4, eb = 7.8

Explanation:

Step1: Recall SAS Similarity Criterion

The SAS (Side - Angle - Side) similarity criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the two triangles are similar. Here, we already know that \(\angle ABC\cong\angle DBE\) (the included angle). So, for SAS similarity, the sides around the included angle (AB, CB for \(\triangle ABC\) and DB, EB for \(\triangle DBE\)) must be proportional.

Step2: Analyze the Options

The options are "greater than", "less than", or "proportional to". Since SAS similarity requires the sides to be proportional (along with the included angle congruence), the correct relationship between AB, CB and DB, EB is that they must be proportional to each other.

Answer:

proportional to