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 theorem for right - triangle congruence requires the hypotenuse and one leg of a right - triangle to be congruent to the hypotenuse and corresponding leg of another right - triangle.

Step2: Identify right - triangles and relevant sides

In right - triangles $\triangle LMP$ and $\triangle NMP$, $MP$ is common. For HL, we need the hypotenuses $ML$ and $MN$ to be equal and $\angle LPM=\angle NPM = 90^{\circ}$. If line $MK$ is the perpendicular bisector of $\overline{LN}$, then $\angle LPM=\angle NPM = 90^{\circ}$ and $LP = NP$. Also, if $ML=MN$, we can prove $\triangle LMP\cong\triangle NMP$ by HL.

Answer:

Line $MK$ is the perpendicular bisector of $\overline{LN}$, $ML = MN$