Question 1019756: given: Angle CED is a right angle, AB congruent to CD, DB bisects AC at E
Prove: Quadrilateral ABCD is a Rhombus
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! 
Discussion of how to prove it:
The goal is to prove that the four right triangles, ΔAED, ΔCED,
ΔAEB, ΔCEB are all congruent. Then all their hypotenuses
will be congruent by CPCT. Begin by showing that all four
angles at E are right angles, making all of four of the
triangles right triangles. Then prove ΔAEB ≅ ΔCED because
AB ≅ CD is given, and since DB bisects AC at E, AE ≅ CE.
Then using DE ≅ DE and BE ≅ BE, you can prove the other
two right triangles congruent.
Edwin
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