Question

use the table below to determine whether triangles abc and edc are similar.
are triangles abc and edc sim

Explanation:

Step1: Check the right - angle pairs

In \(\triangle ABC\) and \(\triangle EDC\), \(\angle ABC = 90^{\circ}\) and \(\angle EDC=90^{\circ}\), so \(\angle ABC\) and \(\angle EDC\) are congruent (\(\angle ABC\cong\angle EDC\)).

Step2: Check the vertical - angle pairs

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

Step3: Use 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. Since we have found two pairs of congruent angles (\(\angle ABC\cong\angle EDC\) and \(\angle BCA\cong\angle DCE\)) in \(\triangle ABC\) and \(\triangle EDC\), the two triangles are similar.

Answer:

Triangles \(ABC\) and \(EDC\) are similar. We know this because \(\angle ABC\cong\angle EDC\) (both are right - angles) and \(\angle BCA\cong\angle DCE\) (vertical angles are congruent), and by the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle EDC\).