Question

statements reasons 1. \\(\overline{de} \parallel \overline{ac}\\) given 2. \\(\angle cab \cong \angle edb\\) \\(\angle acb \cong \angle deb\\) if parallel lines are cut by a transversal, the corresponding angles are congruent. 3. \\(\triangle abc \sim \triangle dbe\\) 4. \\(\frac{ab}{db} = \frac{cb}{eb}\\) milar triangles are proportional 5. \\(ab = ad + db\\) \\(cb = ce + eb\\) 6. \\(\frac{ad + db}{db} = \frac{ce + eb}{eb}\\) substitution property of equality 7. \\(\frac{ad}{db} + 1 = \frac{ce}{eb} + 1\\) division 8. \\(\frac{ad}{db} = \frac{ce}{eb}\\) subtraction property of equality sss criterion for similarity aa criterion for similarity sas criterion for similarity

Explanation:

Step1: Recall triangle similarity criteria

To determine the reason for \(\triangle ABC \sim \triangle DBE\), we analyze the given information. We know two pairs of corresponding angles are congruent (\(\angle CAB \cong \angle EDB\) and \(\angle ACB \cong \angle DEB\)).

Step2: Identify the similarity criterion

The AA (Angle - Angle) criterion for similarity states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Since we have two pairs of congruent corresponding angles, the AA criterion applies here. The SSS criterion requires all three pairs of corresponding sides to be proportional, and the SAS criterion requires two sides to be proportional and the included angle to be congruent, which is not the case here.

Answer:

AA criterion for similarity