Which congruence theorem can be used to prove △bda ≅ △dbc?

hl
sas
aas
sss

A. Hypotenuse-leg (HL) congruence.

Step-by-step explanation:

We have been given a diagram of two right triangles and we are asked to determine the right congruence theorem that will prove △BDA ≅ △DBC.

Since we know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.  

We can see from our diagram that hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.  

We can see that triangles BDA and DBC share a common side DB.

Using Pythagorean theorem we will get,

We have been given that CD=AB, Upon using this information we will get,

Upon subtracting from both sides of our equation we will get,

Therefore, by HL congruence △BDA ≅ △DBC.