As shown in the figure, in trapezoidal ABCD, ad ∥ BC, diagonal AC and BD intersect vertically at O, Mn is the median line of trapezoidal ABCD, ∠ DBC = 30 °, verification: AC = Mn

As shown in the figure, in trapezoidal ABCD, ad ∥ BC, diagonal AC and BD intersect vertically at O, Mn is the median line of trapezoidal ABCD, ∠ DBC = 30 °, verification: AC = Mn

It is proved that: ∵ ad ∥ BC, ∵ ADO = ∠ DBC = 30 °, in RT △ AOD and RT △ BOC, OA = 12ad, OC = 12bc, ∵ AC = OA + OC = 12 (AD + BC), ∵ Mn = 12 (AD + BC), ∵ AC = Mn