Sample Proof on Triangle Congruence Part 2

This is the second part on a series of posts on worked proofs in Triangle Congruence. In this post, we prove another problem.
triangle congruence

Given: \overline{AB} and \overline{CD} bisect each other at E.
Prove: AD \cong BC 

Proof
A bisector divides a segment into equal parts. Now, since AB and CD bisect each other,
AE = BE and CE = DE by definition of bisector.

We also know that
\angle AED \cong \angle CEB because vertical angles are congruent.

triangle congruence2

Now, since the angle is between the congruent sides,
\triangle AED \cong \triangle BEC by SAS congruence.

Therefore, AD \cong BC since corresponding sides of congruent triangles are congruent.

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