Given ∠C ≈ ∠B and ∠BDA is a right angle, are the two triangles, ΔBDA and ΔCDA congruent? If so, by what criterion?

Since angle B and angle C are congruent, angle BDA is a right angle, and the sides of angle B and C have to be congruent, since the angles are congruent, Triangle BDA and Triangle CDA are both congruent, by the Angle-Angle-Side Theorem, which is the criterion that fits this answer.