Question

"What additional information do you need to prove that LMO = LNO by the HL (Hypotenuse-Leg) Theorem?

A) NLO = MLO
B) OM = ON
C) MOL = NOL
D) LM = ML

Select the piece of information that, when added to the given information, would allow you to prove that LMO = LNO using the HL Theorem."

Answer 1

In order to prove that LMO = LNO using the HL (Hypotenuse-Leg) Theorem, we need the information that LM = ML. Option D is correct..

Step-by-step explanation:

In order to prove that LMO = LNO using the HL (Hypotenuse-Leg) Theorem, we need the information that LM = ML. With this additional piece of information, we can establish that the two triangles, LMO and LNO, have a congruent hypotenuse and a congruent leg, which satisfies the conditions of the HL Theorem.

Option B) OM = ON would provide the information needed because it specifically states that both triangles share the same length of hypotenuse (OM and ON being equal) since they share a common vertex at O, and it is implied that LO is the congruent leg common to both triangles.Option D) LM = ML is incorrect since LM and ML refer to the same line segment and thus are inherently equal by definition. Options A) and C) provide information about angles which is not directly relevant to the HL Theorem that requires congruence of sides, specifically the hypotenuse and one leg.