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# Which two Triangles are Congruent?

- Question
- 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)

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