It is known that in the trapezoid ABCD, ad ‖ BC, e and F are the midpoint of AB and CD respectively, connecting EF. Please prove the triangle median theorem according to the method

It is known that in the trapezoid ABCD, ad ‖ BC, e and F are the midpoint of AB and CD respectively, connecting EF. Please prove the triangle median theorem according to the method

Because ad ∥ BC, GA: ab = Gd: DC, because e is the midpoint of AB, f is the midpoint of CD, so Ge: EB = (GA + 1 / 2Ab): (1 / 2Ab) = 2ga: ab + 1 GF: FC = (GD + 1 / 2CD): (1 / 2CD) = 2Gd: CD + 1 = 2ga: ab + 1 = Ge: EB, so EF ∥ BC. Because EF ∥ BC, so HF ∥ BC, eh ∥ ad, and H is the midpoint of BD. according to the triangle median theorem, eh = 1 / 2ad, HF = 1 / 2BC, so EF = 1 / 2 (AD + BC)