Answer:
B. AC ≅ DF and FB ≅ CB
Step-by-step explanation:
The HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Therefore, to prove that right triangles ABC and DBF are congruent using the HL theorem, we would need to know that the hypotenuse and one leg of one triangle are congruent to the corresponding parts of the other triangle.
The hypotenuse of a right triangle is the side opposite the right angle. Therefore, the hypotenuse of triangle ABC is AC, and the hypotenuse of triangle DBF is DF. One of the legs of triangle DBF is FB, and the corresponding leg of triangle ABC is CB.
Therefore, the statement that would be needed to prove the triangles are congruent using the HL theorem is:
[tex]\Large\boxed{\boxed{\sf AC \cong DF\;\; and\;\; FB \cong CB}}[/tex]
