In rectangular trapezoid ABCD, ab ∥ CD, ad ⊥ DC, ab = BC, and AE ⊥ BC

It is proved that the extension of BF ⊥ DC is in F
ABCD is a right angle trapezoid, AB / / CD, ad ⊥ DC
The ABFD is a rectangle,
∴ AD=BF,
∠BCF=∠ABE
And ∵ ∠ AEB = ∠ BFC = 90 °,
∠ABE=∠BCF,AB=BC
Ψ△ AEB ≌ △ BFC (corner side)
∴ AE=BF=AD

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