Question

statements reasons
\\(\overline{ac}\\) bisects \\(\overline{bd}\\) given
\\(e\\) is the mid - point of \\(\overline{ac}\\) given
1 vertical angles
2 definition of mid - point
3 definition of bisector
4 sas
order the statements of the proof based on the figure provided.
\\(\overline{ae}\cong\overline{ce}\\) \\(\overline{be}\cong\overline{de}\\) \\(\triangle aeb\cong\\)

Explanation:

Step1: Use mid - point def.

$\overline{AE}\cong\overline{CE}$

Step2: Use bisector def.

Relevant equal - length segments from $AC$ bisecting $BD$

Step3: Identify vertical angles

For triangles with relevant sides

Step4: Prove $\triangle AEB\cong\triangle CED$ by SAS

Then $\overline{BE}\cong\overline{DE}$

Answer:

1. $\overline{AE}\cong\overline{CE}$
2. (Relevant segments from bisector)
3. (Vertical angles statement)
4. $\overline{BE}\cong\overline{DE}$