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Which two Triangles are Congruent?

Question
how to prove that two triangles are congruent?
In the figure above, AB is parallel to DC, AE = CE. Prove: DE = BE
Solution
since AB // DC (Given)
so angle A = angle C (alternate interior angles are equal)
AE = CE (Given)
angle AEB = angle CED (vertical angles are equal)
so triangle AEB is congruent to triangle CED (angle, side, angle)
so BE = DE (in congruent triangles, congruent angles opposite congruent sides)