∴∠ABC=∠C=72，

∵ ray BD bisects ∠ABC,

∴∠ABD=∠CBD=36。

∴∠BDC=72，

∴AD=BD=BC.

△ dab and △BCD are isosceles triangles. (4 points)

(2) Solution: The vertex angle in figure 1 is divided into 90 degrees, and in figure 2, the vertex angle 108 degrees is divided into 36 degrees and 72 degrees;

(3) Solution: as shown in the figure (just meet the requirements) (5 points)