As shown in the figure, △ ABC is an equilateral triangle with side length L, △ BDC is an isosceles triangle with vertex angle ∠ BDC = 120 ° and makes a 60 ° angle with D as the vertex. The two sides of the angle intersect AB at M and AC at n respectively, and connect Mn to form a triangle. Prove that the perimeter of △ amn is equal to 2

As shown in the figure, △ ABC is an equilateral triangle with side length L, △ BDC is an isosceles triangle with vertex angle ∠ BDC = 120 ° and makes a 60 ° angle with D as the vertex. The two sides of the angle intersect AB at M and AC at n respectively, and connect Mn to form a triangle. Prove that the perimeter of △ amn is equal to 2

It is proved that: as shown in the figure, CM1 = BM is intercepted on the AC extension line, ∵ ABC is an equilateral triangle, ∵ BDC is an isosceles triangle with vertex angle ∵ BDC = 120 degree, ∵ ABC = ACB = 60 degree, ∵ DBC = DCB = 30 degree, ∵ abd = ACD = 90 degree, ∵ dcm1 = 90 degree, ∵ BD = CD, ∵ in ∵ BDM and △ CDM1, BD = CD ≌ abd = dcm1 = 90 ° CM1 = BM, ≌ BDM ≌ CDM1 (SAS), MD = m1d, ≌ MDB = m In △ MDN and △ m1dn, ≌ MDN ≌ m1dn (SAS), Mn = NM1, so the perimeter of △ amn = am + Mn + an = am + an + NM1 = am + AM1 = AB + AC = 2

Given that point C is a point on line AB, AC and BC are taken as edges respectively, and △ ACD and △ BCE are made on the same side of line AB, and Ca = CD, CB = CE, ∠ ACD = ∠ BCE, the line AE and BD intersect at point F,
(1) As shown in Figure 1, if ∠ ACD = 60 °, then ∠ AFB=______ As shown in Figure 2, if ∠ ACD = 90 °, then ∠ AFB=______ As shown in Figure 3, if ∠ ACD = 120 °, then ∠ AFB=______ (2) as shown in Figure 4, if ∠ ACD = α, then ∠ AFB=______ (expressed by the formula containing α); (3) turn △ ACD in Figure 4 clockwise at any angle around point C (the intersection point F is at least on one line segment of BD and AE), as shown in Figure 5. If ∠ ACD = α, what is the quantitative relationship between ∠ AFB and α? And give proof