Question 1019756
{{{drawing(2400/11,400,-1.2,1.2,-2.2,2.2,

line(-1,0,0,2),line(0,2,1,0),line(1,0,0,-2),line(0,-2,0,0),line(-1,0,0,-2),
line(-1,0,1,0), line(0,2,0,-2), locate(-1.15,.1,A),locate(1.05,.1,C),
locate(0.05,0,E),locate(0,2.15,D),locate(0,-2,B) )}}}

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</pre>