Question

read the proof. given: (overline{ab} parallel overline{de}) prove: (\triangle abc sim \triangle edc) diagram of points a, b, c, d, e with triangles

statement	reason
2. (angle acb) and (angle ecd) are vert. (angle)s	2. definition of vertical angles
3. (angle acb cong angle dce)	3. vertical angles are congruent
4. (angle bde) and (angle dba) are alt. int. (angle)s	4. definition of alternate interior angles
5. (angle bde cong angle dba)	5. alternate interior angles are congruent
6. (\triangle abc sim \triangle edc)	6. ?

options: aa similarity theorem, asa similarity theorem, aas similarity theorem, sas similarity theorem

Explanation:

To prove \(\triangle ABC \sim \triangle EDC\), we check the angles. We have \(\angle ACB \cong \angle DCE\) (vertical angles) and \(\angle BDE \cong \angle DBA\) (alternate interior angles). The AA (Angle - Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Here, two pairs of angles are congruent, so we use the AA similarity theorem.

Answer:

AA similarity theorem