Question

Triangles L M N and L K N are connected at side L N. A line is drawn from point M to point K and intersects side L N at point P.
Examine this figure. Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP 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

Answer 1

Selections:
- Line MK is the perpendicular bisector of LN.
- ML ≅ MN.

Reason: If MK is the perpendicular bisector of LN, then MP (on MK) is perpendicular to LN so ∠LPM and ∠NPM are right angles. With ML ≅ MN (equal hypotenuses) and MP common (equal leg), ΔLMP ≅ ΔNMP by HL.