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 midpoint of mk. line mk is the perpendicular bisector of ln. ml≅mp ml≅mn pk≅pk

Explanation:

Step1: Recall HL - Hypotenuse - Leg

HL (Hypotenuse - Leg) congruence criterion for right - triangles 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.

Step2: Analyze given figure

In \(\triangle LMP\) and \(\triangle NMP\), we need to identify right - angles and congruent sides. If line \(MK\) is the perpendicular bisector of \(\overline{LN}\), then \(\angle LPM=\angle NPM = 90^{\circ}\) and \(LP = NP\). Also, \(\overline{MP}\) is common to both triangles. For HL, we need the hypotenuses to be congruent. If \(\overline{ML}\cong\overline{MN}\), then in right - triangles \(\triangle LMP\) and \(\triangle NMP\), the hypotenuses are congruent and one leg (\(\overline{MP}\)) is common.

Answer:

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