A perpendicular line is constructed through angle B of Triangle ABC and intersects side AC at a 90° angle through point D.

Select the transformations that would justify that Triangles ABD and CBD are congruent. Select all that apply.

A. A reflection over BD that maps AB onto BC.

B. A translation along vector AC that maps point A onto point C.

C. A rotation about center B that maps BD of Triangle CBD onto BA.

D. A rotation about center D that maps BD of Triangle CBD onto AD and angle BDC onto angle ADB.

E. A rotation about center D that maps CD onto AD. Then a reflection across AD that maps angle ABD onto angle CBD.