Question

which congruence theorem can be used to prove △bda ≅ △dbc?
options: hl, sas, aas, sss

Explanation:

Step1: Identify the triangles as right - angled

$\triangle BDA$ and $\triangle DBC$ are right - angled triangles (right angles at the marked vertices).

Step2: Check the hypotenuse and leg

The hypotenuse ($BD$ is common to both triangles, so hypotenuse is equal) and one leg (the marked equal sides in the diagram). By the Hypotenuse - Leg (HL) congruence theorem for right - angled triangles, $\triangle BDA\cong\triangle DBC$.

Answer:

HL