Question

step statement reason 1 ab ≅ cd given bc ≅ ad 2 ac ≅ ac reflexive property 3 △abc ≅ △cda sss 4 ∠bca ≅ ∠cad vertical angles are congruent 5 ∠bec ≅ ∠dea select a reason... note: ac and bd are segments. answer attempt 2 out of 2 you must answer all questions above in order to submit.

Explanation:

Step1: Identify given information

Given \(AB\cong CD\), \(BC\cong AD\) and \(AC\cong AC\)

Step2: Apply congruence postulate

By SSS (Side - Side - Side) postulate, \(\triangle ABC\cong\triangle CDA\) since all three pairs of corresponding sides are congruent.

Step3: Analyze angles

\(\angle BCA\) and \(\angle CAD\) are not vertical angles. They are corresponding angles of congruent triangles \(\triangle ABC\) and \(\triangle CDA\) due to the congruence \(\triangle ABC\cong\triangle CDA\).

Step4: Reason for \(\angle BEC\cong\angle DEA\)

\(\angle BEC\) and \(\angle DEA\) are vertical angles. Vertical angles are always congruent. So the reason for \(\angle BEC\cong\angle DEA\) is "Vertical angles are congruent".

Answer:

The reason for \(\angle BEC\cong\angle DEA\) is "Vertical angles are congruent".