Question

Which congruence theorem can be used to prove △BDA ≅ △DBC? HL SAS AAS SSS

Answer 1

HL, when you have 2 right triangles and their hypotenuses are congruent you are able to say HL

Answer 2

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,

$CD^{2}=DB^{2}+BC^{2}...(1)$  

$AB^{2}=DB^{2}+AD^{2}...(2)$

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

$DB^{2}+BC^{2}=DB^{2}+AD^{2}$

Upon subtracting $DB^{2}$ from both sides of our equation we will get,

$BC^{2}=AD^{2}$

$BC=AD$

Therefore, by HL congruence △BDA ≅ △DBC.