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Answer:
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,
[tex]CD^{2}=DB^{2}+BC^{2}...(1)[/tex]
[tex]AB^{2}=DB^{2}+AD^{2}...(2)[/tex]
We have been given that CD=AB, Upon using this information we will get,
[tex]DB^{2}+BC^{2}=DB^{2}+AD^{2}[/tex]
Upon subtracting [tex]DB^{2}[/tex] from both sides of our equation we will get,
[tex]BC^{2}=AD^{2}[/tex]
[tex]BC=AD[/tex]
Therefore, by HL congruence △BDA ≅ △DBC.
