Question

given △abc and △dec with congruent parts as marked, what else is needed to show congruence? complete the sentences below. if ab ≅ then there is congruence by asa. alternatively, to use aas, either of the conditions bc ≅ ec or ac ≅ is needed.

Explanation:

Step1: Recall ASA congruence

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. We already have two pairs of angles congruent. For ASA, we need the included sides to be congruent. The included side between the given angles for \(\triangle ABC\) and \(\triangle DEC\) is \(AC\) and \(DC\). So if \(AC\cong DC\), there is congruence by ASA.

Step2: Recall AAS congruence

AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent. We have two pairs of angles congruent. For AAS, we can either have \(BC\cong EC\) or \(AC\cong DC\).

Answer:

If \(AC\cong DC\), then there is congruence by ASA. Alternatively, to use AAS, either of the conditions \(BC\cong EC\) or \(AC\cong DC\) is needed.