As shown in the figure, it is known that △ ABC is an isosceles right triangle, ∠ BAC = 90 °, be is the bisector of ∠ ABC, de ⊥ BC, and the perpendicular foot is d. (1) please write all isosceles triangles in the figure; (2) please judge whether AD is perpendicular to be? (3) if BC = 10, find the length of AB + AE

As shown in the figure, it is known that △ ABC is an isosceles right triangle, ∠ BAC = 90 °, be is the bisector of ∠ ABC, de ⊥ BC, and the perpendicular foot is d. (1) please write all isosceles triangles in the figure; (2) please judge whether AD is perpendicular to be? (3) if BC = 10, find the length of AB + AE

(1) (2) ad is perpendicular to be. It is proved that if be is the bisector of ∠ ABC, ∠ Abe = ∠ DBE, ∠ BAE = ∠ BDE = 90 ° be = be, be is folded along be and must coincide with △ DBE