Which congruence theorem can be used to prove △BDA ≅ △DBC? Triangles B D A and D B C share side D B. Angles C B D and A D B are right angles. Sides C D and B A are congruent. HL SAS AAS SSS

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.

hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.

BDA and DBC share a common side DB.

Using Pythagorean theorem we will get,

[tex]CD^{2}=DB^{2}+BC^{2}...(1) \\\\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}\\\\BC=AD[/tex]

Therefore, by HL congruence △BDA ≅ △DBC.

MrRoyal MrRoyal · Answer 2 · 2021-10-11T16:01:09+02:00

There are several congruence theorems that can be used to prove the congruence of triangles.

The congruence theorem to prove [tex]\mathbf{\triangle BDA \cong \triangle DBC}[/tex] is: (a) Hypotenuse Leg (HL)

From the complete question (see attachment), we have the following observations

The hypotenuse of triangles BDA and DBC are the same.
Both triangles have a corresponding right-angle

When two triangles have an equal hypotenuse, then the congruence of both triangles can be proved by Hypotenuse Leg theorem

Hence, the congruence theorem to prove [tex]\mathbf{\triangle BDA \cong \triangle DBC}[/tex] is: (a) Hypotenuse Leg (HL)

Read more about congruence theorems at:

https://brainly.com/question/19568627