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 congruence

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

Step2: Analyze the options for right - triangle congruence

If point P is the mid - point of MK, then MP = PK. In right - triangles LMP and NMP, if we can show that the hypotenuse (ML and MN) and one leg (MP) are congruent, we can use HL. Also, if line MK is the perpendicular bisector of LN, then ∠LPM=∠NPM = 90°, and we have right - triangles. And if ML = MN (hypotenuse) and MP is common (leg), we can prove congruence by HL.

Answer:

Line MK is the perpendicular bisector of LN, Point P is the midpoint of MK