SOLUTION: How do you prove that AKCE is a parallelogram when the given is, parallelogram ABCD, E&K on diagnal BD, and DE=BK?

Algebra ->  Geometry-proofs -> SOLUTION: How do you prove that AKCE is a parallelogram when the given is, parallelogram ABCD, E&K on diagnal BD, and DE=BK?      Log On


   

Question 416260: How do you prove that AKCE is a parallelogram when the given is, parallelogram ABCD, E&K on diagnal BD, and DE=BK?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A quadrilateral is a parallelogram if and only if the diagonals bisect each other.
You will have to apply triangle+congruency here.
Consider the two opposite triangles made by the diagonal;they are congruent by SAS congruency since two sides which were bisected were equal and the interior opposite angles made by the diagonals.
Now proving both the set of opposite triangles+congruent you will get opposite+sides+equal which is enough to prove that the quadrilateral is a parallelogram.