Question

what additional statement could you use to prove that △bjk≅△cfh by the hl theorem?
○ bj = cf
○ ∠b≅∠c
○ jk≅fh
○ ∠bjk≅∠cfh

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

HL theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. In right - triangles $\triangle BJK$ and $\triangle CFH$, we need to have the hypotenuses and one pair of legs congruent.

Step2: Analyze the options

• Option $\overline{AB}\cong\overline{AC}$ gives information about the sides of $\triangle ABC$ and not directly about the right - triangles $\triangle BJK$ and $\triangle CFH$.
• Option $\angle B\cong\angle C$ is an angle - congruence statement. HL theorem requires side - congruence, so this is not relevant.
• Option $\overline{JK}\cong\overline{FH}$ gives the congruence of one pair of legs. If we also know that the hypotenuses (implicitly related to the sides of $\triangle ABC$) are congruent in a way that can be established from the context of the whole triangle, this can be used in HL.
• Option $\angle BJK\cong\angle CFH$ is an angle - congruence statement and not useful for HL theorem which is for right - triangles and requires side - congruence.

Answer:

$\overline{JK}\cong\overline{FH}$