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BlakeMATH
The reason that ABD and ACB are similar is because of ASA (angle-side-angle). They share both the line AB and two congruent angles, <C and <B.

Answer with explanation:

In Δ A B D and ΔA CB

1.   ⇒ ∠ A is Common.

2.⇒ ∠ABD=∠ACB=45°------[Given]

⇒Δ A B D ~ ΔA CB------[Angle-Angle Similarity Axiom abbreviated as (AA)]