Question

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

Explanation:

Step1: Find the reason for $\overline{BE}\cong\overline{ED}$

Since $\overline{AC}$ bisects $\overline{BD}$, by the definition of a bisector, it divides the segment into two equal parts. So, $\overline{BE}\cong\overline{ED}$ because of the definition of a bisector.

Step2: Find the reason for $\angle B\cong\angle D$

From the figure, $\angle B$ and $\angle D$ are marked as equal. So, $\angle B\cong\angle D$ because of the given markings in the diagram.

Step3: Find the reason for $\angle A\cong\angle C$

From the figure, $\angle A$ and $\angle C$ are marked as equal. So, $\angle A\cong\angle C$ because of the given markings in the diagram.

Step4: Find the reason for $\triangle ABE\cong\triangle CDE$

We have $\overline{BE}\cong\overline{ED}$ (from Step1), $\angle B\cong\angle D$ (from Step2), and $\angle A\cong\angle C$ (from Step3). By the Angle - Angle - Side (AAS) congruence criterion, $\triangle ABE\cong\triangle CDE$.

Answer:

• $\overline{BE}\cong\overline{ED}$: Definition of a bisector
• $\angle B\cong\angle D$: Given (from diagram markings)
• $\angle A\cong\angle C$: Given (from diagram markings)
• $\triangle ABE\cong\triangle CDE$: AAS (Angle - Angle - Side) congruence criterion