As shown in the figure, in ladder ABCD, ad ‖ BC and EF are the midpoint of AB and AC respectively. Connect EF and intersect AB and CD with G and h to verify: (1) eh = GF; (2) Hg = 1 / 2 (BC-AD)

As shown in the figure, in ladder ABCD, ad ‖ BC and EF are the midpoint of AB and AC respectively. Connect EF and intersect AB and CD with G and h to verify: (1) eh = GF; (2) Hg = 1 / 2 (BC-AD)

（1）
E is the midpoint of AB and F is the midpoint of CD
∴EF∥AD
The EG is the median line of △ abd
∴EG=1/2AD
Similarly, FH = 1 / 2ad
∴EG =FH
(2)
Connect Ag and extend, and cross BC to point M
∵∠ ADG = ∠ MBG, ∠ AGD = ∠ MGB, Ag = Mg (eg is the median line of △ ABM)
∴△ADG≌△BMG(AAS)
∴AD=BM
According to (1), GH is the median of △ AMC
∴GH=1/2MC=1/2(BC-BM)=1/2(BC-AD)