Question

copy the triangles and highlight congruent parts. mark and highlight additional congruent parts that can be proven. explain why the parts are congruent. state how the triangles can be proven congruent, if possible. alternate interior angles are congruent, aaa, not congruent alternate interior angles are congruent, ssa, not congruent vertical angles congruent, aas vertical angles congruent, sas

Explanation:

Step1: Identify congruent parts

Vertical angles are congruent. In the figure, \(\angle DEC\) and \(\angle BEA\) are vertical angles. So, \(\angle DEC\cong\angle BEA\).

Step2: Use given side - side congruence

From the markings, \(DE = BE\) and \(CE=AE\).

Step3: Apply congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In \(\triangle DEC\) and \(\triangle BEA\), \(DE = BE\), \(\angle DEC=\angle BEA\), \(CE = AE\). So, \(\triangle DEC\cong\triangle BEA\) (SAS).

Answer:

Vertical angles congruent, SAS.