Final answer:
The HL Congruence Theorem explains the congruence of right triangles ABD and CBD since they share a hypotenuse and have a congruent leg.
Step-by-step explanation:
The theorem that justifies the congruence of right triangles ABD and CBD is the HL (Hypotenuse-Leg) Congruence Theorem, which states that two right triangles are congruent if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of the other triangle.
In this case, since triangle ABD is congruent to triangle CBD, and they are both right triangles, they share the hypotenuse (BD) and have another congruent side by definition of congruent triangles (AD = CD as ABD is congruent to CBD).