Final answer:
Without additional information, we cannot confidently choose a congruence criterion to prove triangles ABD and CBD are congruent. However, based on common elements and if certain angles or sides are equal, the SAS, ASA, or AAS criteria might apply.
The correct answer is none of above.
Step-by-step explanation:
To determine which congruence criterion can be used to show that triangles ABD and CBD are congruent, we need to analyze what is given or can be deduced about the triangles. Since AB is shared by ABD and CBD, we have one side in common. If angle ABD is equal to angle CBD, we have an angle in common. Finally, if AD and CD are of equal length, we have the SAS (Side-Angle-Side) criterion because we have two sides and the included angle equal.
However, without additional information or a diagram, we cannot be certain which criterion applies. When we have two angles and a non-included side equal in two triangles, we use the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria. The choice depends on the position of the equal side in relation to the equal angles.