Question

drag & drop the answer def. of bisector def. of midpoint given reflexive property def. of vertical angles sss sas asa aas cpctc

Explanation:

Step1: Analyze \(\overline{AC}\cong\overline{EC}\)

This is likely given as a starting - point in a geometric proof. So, it is "Given".

Step2: Analyze \(\angle BCA\cong\angle DCE\)

Vertical angles are formed when two lines intersect. \(\angle BCA\) and \(\angle DCE\) are vertical angles. By the definition of vertical angles, \(\angle BCA\cong\angle DCE\).

Step3: Analyze \(\overline{BC}\cong\overline{DC}\)

This is likely given as a starting - point in a geometric proof. So, it is "Given".

Step4: Analyze \(\triangle ABC\cong\triangle EDC\)

We have two sides and the included angle (\(\overline{AC}\cong\overline{EC}\), \(\angle BCA\cong\angle DCE\), \(\overline{BC}\cong\overline{DC}\)). By the SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle EDC\).

Step5: Analyze \(\angle A\cong\angle E\)

Since \(\triangle ABC\cong\triangle EDC\), corresponding parts of congruent triangles are congruent. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\angle A\cong\angle E\).

Answer:

\(\overline{AC}\cong\overline{EC}\) - Given; \(\angle BCA\cong\angle DCE\) - Def. of Vertical Angles; \(\overline{BC}\cong\overline{DC}\) - Given; \(\triangle ABC\cong\triangle EDC\) - SAS; \(\angle A\cong\angle E\) - CPCTC