So △ADE is an isosceles triangle, ∠ EDA = 120, then ∠ EAC = 30, ∠ ECA = 30, then △EAC is an isosceles triangle, then EC = AE.

∠BAE=∠BAC-∠EAC=45 -30 = 15

∠ bea = 150, then∠ Abe =180-150-15 =15 = ∠ Abe, △AEB is an isosceles triangle.

EC=AE=BE, then △BEC is an isosceles right triangle.

2.△AED is similar to △△CAE；; △ABC is similar to△△ CBD;

3. The area ratio of △ BEC to △BEA is 2:1;