Question

ac bisects bd
reason:
given
be ≅ ed
reason:
select reason
∠a ≅ ∠c
reason:
select reason
∠bea ≅ ∠ced
reason:
select reason
△abe ≅ △cde
reason:
select reason

Explanation:

Step1: Reason for \( \overline{BE}\cong\overline{ED} \)

Since \( \overline{AC} \) bisects \( \overline{BD} \), by the definition of a bisector.

Step2: Reason for \( \angle A\cong\angle C \)

Given in the problem statement.

Step3: Reason for \( \angle BEA\cong\angle CED \)

Vertical angles are congruent.

Step4: Reason for \( \triangle ABE\cong\triangle CDE \)

By the Angle - Side - Angle (ASA) congruence criterion.

Answer:

\(\overline{BE}\cong\overline{ED}\) Reason: Definition of a bisector; \(\angle A\cong\angle C\) Reason: Given; \(\angle BEA\cong\angle CED\) Reason: Vertical angles are congruent; \(\triangle ABE\cong\triangle CDE\) Reason: ASA (Angle - Side - Angle)