Question

examine this figure. which two pieces of information, if true, would help to prove that △lmp≅△nmp by hl? select two options. point p is the mid - point of mk. line mk is the perpendicular bisector of ln. ml≅mp ml≅mn pk≅pk

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

HL theorem states that in two right - triangles, if the hypotenuse and one leg are congruent, the triangles are congruent. In \(\triangle LMP\) and \(\triangle NMP\), \(\overline{MP}\) is common.

Step2: Analyze the hypotenuse

For \(\triangle LMP\) and \(\triangle NMP\), if \(MK\) is the perpendicular bisector of \(\overline{LN}\), then \(\angle MPL=\angle MPN = 90^{\circ}\) and \(\overline{LP}=\overline{NP}\). Also, if \(\overline{ML}\cong\overline{MN}\), \(\overline{ML}\) and \(\overline{MN}\) are the hypotenuses of \(\triangle LMP\) and \(\triangle NMP\) respectively and \(\overline{MP}\) is the common leg.

Answer:

Line MK is the perpendicular bisector of \(\overline{LN}\), \(\overline{ML}\cong\overline{MN}\)