Question 1034179
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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 <A HREF=https://www.algebra.com/algebra/homework/Parallelograms/Properties-of-diagonals-of-parallelograms.lesson>Properties of diagonals of parallelograms</A> 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.