Given: AD bisects BC at E; AB is parallel to CD

Prove: Triangle ABE is congruent to Triangle CDE

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Parallel lines form equal alternate interior angles
Vertical angles are equal
AD bisects BC at E; AB is parallel to CD
angle AEB is congruent to angle CED
BE is congruent to CE
ASA (Angle-Side-Angle)
angle B is congruent to angle C
Triangle ABE is congruent to Triangle CDE
Given
Definition