1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)
4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)
9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)
10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
