"bisect" means "split in half"
BD and AC bisect each other, so the smaller pieces are congruent.
BD splits to BE = ED
AC splits to AE = EC
Draw tickmarks to indicate which segments are congruent. Refer to the diagram below. The single tickmark segments pair up, and so do the double tickmark segments.
Notice how angle AEB = angle CED because of they are vertical angles.
We have enough information to conclude the triangles are congruent. We use the SAS congruence theorem.
SAS = side angle side
In the diagram below I use color coding to show how the congruent sides pair up.