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As shown in the figure, in ladder ABCD, ad ∥ BC, ∠ DCB = 45 °, CD = 2, BD ⊥ CD. Through point C, make CE ⊥ AB to e, intersect diagonal BD to F, point G is the midpoint of BC, connect eg and AF. (1) calculate the length of eg; (2) verify: CF = AB + AF
(1) In RT △ BDC, BC = DB2 + CD2 = 22, ∵ CE ⊥ be, ∵ BEC = 90 °, ∵ point G is the midpoint of BC, ∵ eg = 12bc = 2 (the property of the midline on the hypotenuse of a right triangle)
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