Question

what additional information do you need to prove that △lmo≅△lno by the hl theorem?
o (overline{om}=overline{on})
o (angle molcongangle nol)
o (angle nlocongangle mlo)
o (overline{lm}=overline{ml})

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

The HL 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 two right - triangles are congruent. In right - triangles $\triangle LMO$ and $\triangle LNO$, $\overline{LO}$ is common (hypotenuse). We need to show that one of the legs is congruent.

Step2: Analyze the options

Among the given options, $\overline{OM}=\overline{ON}$ would give us the congruence of one leg of the two right - triangles. $\angle MOL\cong\angle NOL$ and $\angle NLO\cong\angle MLO$ are angle - related and not relevant for HL. $\overline{LM}=\overline{ML}$ is just a self - congruence of a non - relevant side for HL in this context.

Answer:

$\overline{OM}=\overline{ON}$