Question

determine which triangle congruence theorem explains how the triangles are congruent. side - side - side congruence theorem angle - side - angle congruence theorem side - angle - side congruence theorem angle - angle - side congruence theorem

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. So, \(\angle BCA\cong\angle DCE\).

Step2: Analyze given congruent parts

We are given \(AC = DC\) (marked as equal), \(\angle A=\angle D\) (marked as equal), and from Step 1 \(\angle BCA=\angle DCE\).

Step3: Recall congruence theorems

The Angle - Side - Angle (ASA) Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Here, \(\angle A\), \(AC\), \(\angle BCA\) in \(\triangle ABC\) correspond to \(\angle D\), \(DC\), \(\angle DCE\) in \(\triangle DEC\) respectively.

Answer:

Angle - Side - Angle Congruence Theorem