Question

use the table below to determine whether triangles abc and edc are similar.
are triangles abc and edc similar? cannot be determined

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

The AA similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Step2: Analyze the given angle - pair congruency

We know that \(\angle ABC\) and \(\angle EDC\) are congruent (both are right - angles, and all right - angles are congruent). If we can find another pair of congruent angles, we can apply the AA criterion.

Step3: Consider the vertical - angle property

\(\angle BCA\) and \(\angle DCE\) are vertical angles. By the vertical - angles theorem, vertical angles are congruent.

Answer:

Triangles \(ABC\) and \(EDC\) are similar. The reason is that \(\angle ABC\cong\angle EDC\) (all right - angles are congruent) and \(\angle BCA\cong\angle DCE\) (vertical angles are congruent). So, by the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle EDC\)