As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at O, e and F are the midpoint of OA and ob respectively. (1) prove: △ ade ≌ △ BCF; (2) if ad = 4cm, ab = 8cm, find the length of CF

As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at O, e and F are the midpoint of OA and ob respectively. (1) prove: △ ade ≌ △ BCF; (2) if ad = 4cm, ab = 8cm, find the length of CF

(1) The following proofs have been proved: the four quadrilateral ABCD is a rectangle, ad = BC, OA = OC, OB = OD, AC = BD, ad \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\f From (1), we can see that f is the midpoint of ob, so DF = 3fb, dfdb = 34  fg4 = 34 = dg8 〉 FG = 3, DG = 6 〉 GC = dc-dg = 8-6 = 2 in RT △ FGC, CF = fg2 + GC2 = 9 + 4 = 13cm. (note: other solutions can refer to the given points, such as extending CF to point h, using △ DFC ∽ BFH to calculate.)