Question

what additional information do you need to prove that △lmx≅△lox by the hl theorem?
o mn≅lo
o lm≅lo
o lm≅on
o lx≅xn

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

The HL theorem states that in two right - triangles, if the hypotenuse and one leg are congruent, then the triangles are congruent. In right - triangles $\triangle LMX$ and $\triangle OMX$, $\angle LXM=\angle OXM = 90^{\circ}$ (given by the right - angle symbol at $X$). The common side $MX$ is a leg for both triangles. We need the hypotenuses of the two right - triangles to be congruent.

Step2: Analyze the options

We know that in right - triangles $\triangle LMX$ and $\triangle OMX$, if $LM = LO$, then by the HL theorem, $\triangle LMX\cong\triangle OMX$.

Answer:

B. $\overline{LM}\cong\overline{LO}$