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

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.