As shown in the figure, the side length of square ABCD is 2, point E is the midpoint of BC side, BG ⊥ AE is made through point B, the perpendicular foot is g, extend BG to intersect AC at point F, then CF=______ ．

In square ABCD, the side length of a square is 2. According to Pythagorean theorem, we obtain AC = 22. ∵ AB = BC, ∵ Abe = ≌ BCH = 90 °, BAE = ≌ CBH, ≌ Abe ≌ BCH, ≌ ch = be = 1. ∵ ab ∥ CD, ∥ Abf ∥ CHF, ∥ afcf = abch = 2, ≌ CF = 13ac = 223

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