Question

what else is needed to prove these triangles congruent using the hl theorem? ∠f ≅ ∠b and ac ≅ dc. bc ≅ fc. nothing else is needed to use the hl theorem.

Explanation:

Step1: Recall HL Theorem

HL (Hypotenuse - Leg) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Step2: Identify Right Triangles

Triangles \( \triangle ABC \) and \( \triangle DFC \) are right triangles (since \( \angle A \) and \( \angle D \) are right angles). We know \( AB \cong DF \) (marked by the same tick marks on the legs).

Step3: Determine Missing Part for HL

For HL, we need the hypotenuses to be congruent. The hypotenuses of \( \triangle ABC \) and \( \triangle DFC \) are \( BC \) and \( FC \) respectively. So we need \( BC \cong FC \). The other options either use non - HL criteria or are incorrect as we do need the hypotenuse congruence here.

Answer:

\( BC \cong FC \)