The congruence theorem that will prove △BDA and △DBC is A. Hypotenuse-leg (HL) congruence.
Determining the right congruence theorem that will prove △BDA and △DBC after being provided a schematic of two right triangles.
Since we are aware that the hypotenuse-leg theorem stipulates that if the hypotenuse and one of the right triangles' legs are congruent with their equivalent hypotenuses in other right triangles, the triangles are said to be 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
CD² = DB²+BC²
AB = DB²+AD²
given that CD=AB, Upon using this information we will get,
DB²+BC² = DB²+AD²
subtracting DB² from both sides of our equation we will get,
BC² = AD²
Cutting squares on both sides
BC = AD
Hence, by HL congruence △BDA ≅ △DBC.
Note that the full question is:
Which congruence theorem can be used to prove △BDA ≅ △DBC?
A. HL
B. SAS
C. AAS
D. SSS
To learn more about Hypotenuse-leg congruence: https://brainly.com/question/29615095
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