SOLUTION: Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E. Prove: triangle AED is congruent to triangle CEB.

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Question 1034179: Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E. Prove: triangle AED is congruent to triangle CEB.
Found 2 solutions by fractalier, ikleyn:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
1) State the given.
2) Opposite sides of a parallelogram are equal.
3) Show how the diagonals are transversals between parallel sides.
4) Show how two pairs of corresponding angles are alternate interior angles and congruent.
5) State congruency by ASA.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E. Prove: triangle AED is congruent to triangle CEB.
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In a parallelogram, the diagonals bisect each other.
See the lesson Properties of diagonals of parallelograms in this site.

So, the triangles AED and CEB have two congruent sides: AE = EC and DE = EB.

The angles between these sides are congruent as vertical angles.

Hence, the triangles AED and CEB are congrurnt, in accordance with SAS-test.