As shown in the figure, in ladder ABCD, ad ‖ BC, e is the midpoint of CD, AE ⊥ be, ab = AD + BC

As shown in the figure, in ladder ABCD, ad ‖ BC, e is the midpoint of CD, AE ⊥ be, ab = AD + BC

Take the midpoint f on AB and connect EF
∵ in ladder ABCD, e and F are the midpoint of DC and ab respectively
∴EF=1/2(AD+BC)
In RT △ AEB, f is the midpoint of the hypotenuse ab
∴FE=1/2AB
∴EF=1/2(AD+BC)=1/2AB
∴AD+BC=AB