In △ ABC, ab = AC, CG ⊥ Ba intersects the extension line of BA at point g. an isosceles right triangle ruler is placed as shown in Figure 1. The right angle vertex of the triangle ruler is F. one right angle side is in a straight line with AC side, and the other right angle side just passes through point B (1) In Figure 1, please guess and write down the quantitative relationship between BF and CG by observing and measuring the length of BF and CG, and then prove your conjecture; (2) when the triangle ruler moves to the position shown in Figure 2 along the direction of AC, one right angle side is still on the same line with AC side, the other right angle side intersects BC side at point D, and makes de ⊥ BA at point e through point D. at this time, please observe and measure De, D The length of F and CG, conjecture and write the quantitative relationship between de + DF and CG, and then prove your conjecture; (3) whether the conjecture in (2) is still true when the triangle ruler continues to move to the position shown in Fig. 3 along the direction of AC on the basis of (2) (the point F is on the line AC, and the point F does not coincide with point C) (do not explain the reason)

In △ ABC, ab = AC, CG ⊥ Ba intersects the extension line of BA at point g. an isosceles right triangle ruler is placed as shown in Figure 1. The right angle vertex of the triangle ruler is F. one right angle side is in a straight line with AC side, and the other right angle side just passes through point B (1) In Figure 1, please guess and write down the quantitative relationship between BF and CG by observing and measuring the length of BF and CG, and then prove your conjecture; (2) when the triangle ruler moves to the position shown in Figure 2 along the direction of AC, one right angle side is still on the same line with AC side, the other right angle side intersects BC side at point D, and makes de ⊥ BA at point e through point D. at this time, please observe and measure De, D The length of F and CG, conjecture and write the quantitative relationship between de + DF and CG, and then prove your conjecture; (3) whether the conjecture in (2) is still true when the triangle ruler continues to move to the position shown in Fig. 3 along the direction of AC on the basis of (2) (the point F is on the line AC, and the point F does not coincide with point C) (do not explain the reason)

(1) BF = CG; prove: in △ ABF and △ ACG, ∵ f = ∠ g = 90 °, ∵ Fab = ∠ GAC, ab = AC ≌ Abf ≌ ACG (AAS) ≌ BF = CG; (2) de + DF = CG; prove: through point D as DH ⊥ CG at point H (as shown in Fig. 2) ∵ de ⊥ BA at point E, ≁ g = 90 °, DH ⊥ CG ≌ edgg as rectangle ≁ de =