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Y_Kistochka [10]

2 years ago

5

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

2 answers:

Tomtit [17]2 years ago

6 0

Answer:

A. Hypotenuse-leg (HL) congruence.

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

Step-by-step explanation:

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,

$CD^{2}=DB^{2}+BC^{2}...(1) \\\\AB^{2}=DB^{2}+AD^{2}...(2)$

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,

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

<h3>Therefore, by HL congruence △BDA ≅ △DBC.</h3>

Westkost [7]2 years ago

3 0

Answer:

D)SSS hope this helps

Step-by-step explanation:

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