Let AE and DC intersect at F.
Because △ Abe △ ACD
So ∠ AEB = ∠ ADC.
Because < AFD = < CFE
So ∠ECF=∠DAF.
(If two sets of angles in two triangles are equal, the other set of angles must be equal. )
Because ∠ DAF = ∠ DAE = 90 degrees
So ∠ ECF = 90 degrees, that is ∠ ECD = 90 degrees.
So DC⊥BE
For reference! (JSWYC)