Question

do we have enough information to say these two triangles are congruent? if so, what allows us to say this?

Explanation:

Step1: Check the congruence criteria

We have two right - angled triangles (∠ADB and ∠CDB are right angles). The hypotenuse (AB = CB, as marked with the same length) and the leg (BD is common to both triangles).

Step2: Apply the HL (Hypotenuse - Leg) criterion

For right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent.

Answer:

Yes, HL