In a rectangle ABCD, E is a point which bisects BC, prove AE=ED

Given - ABCD is a rectangle .
E is a point on BC such that BE=EC .
To prove - AE=AD
Proof- In triangle ABE and DCE
AB = DC ( ABCD is a rectangle )
Angle E =Angle D ( Each 90)
BE = CE (Given)
So by SAS Congruency theorem ABE is congruent to DCE
Therefore by CPCT , AE = AD
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Isn't it angle C = angle B (90 degree each)?
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