Question

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

o side-angle-side congruence theorem
o side-side-side congruence theorem
o angle-side-angle congruence theorem
o angle-angle-side congruence theorem

Explanation:

Step1: Identify vertical angles

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

Step2: Analyze side - angle - side

From the markings, \(AC = DC\), \(BC = EC\), and \(\angle ACB=\angle DCE\). By the Side - Angle - Side (SAS) Congruence Theorem, \(\triangle ABC\cong\triangle DEC\).

Answer:

Side - Angle - Side Congruence Theorem