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) congruence criterion

HL is used for right - triangles where the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle.

Step2: Analyze the figure for right - triangles and relevant segments

In right - triangles $\triangle LMP$ and $\triangle NMP$, we need the hypotenuse and a leg to be congruent. If $ML\cong MN$ (this gives us the hypotenuse congruence as $ML$ and $MN$ can be considered as hypotenuses of right - triangles $\triangle LMP$ and $\triangle NMP$ respectively) and point $P$ is the mid - point of $MK$ (so $LP = NP$ as the perpendicular from the vertex to the base of an isosceles triangle $\triangle LMN$ bisects the base, and also gives us congruent legs), we can prove $\triangle LMP\cong\triangle NMP$ by HL.

Answer:

1. $ML\cong MN$
2. Point $P$ is the mid - point of $MK$