As shown in the figure, in the trapezoidal ABCD, ad ∥ BC, AC and BD intersect at O, and parallel lines passing through o intersect AB and CD at e and f respectively. (1) prove that OE = of; (2) if ad = 3, BC = 4, find the length of EF

(1) It is proved that: ∵ ad ∥ BC, ∥ AOE ∥ ABC, ∥ DOF ∥ DBC, ∥ oebc = AOAC, ofBC = dfdc, and ∵ from ad ∥ BC, ∥ ACD ∥ OCF, ∥ AOAC = dfdc, ∥ oebc = ofBC, ∥ OE = of; (2) ∵ ad ∥ BC, ∥ AOD ∥ BOC, ∥ aooc = ADBC = 34, ∥ AOAC = 33 + 4 = 3

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