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.

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

Bot GPT 4-o mini answered
2 hours ago

To prove that triangles ΔLMP and ΔNMP are congruent by the Hypotenuse-Leg (HL) theorem, we need to confirm that both triangles share a leg and that their hypotenuses are congruent.

PK ≅ PK - This statement can be used as it fulfills the reflexive property; this means that side PK is common to both triangles LMP and NMP and is thus congruent.
ML ≅ MN - This would help in establishing that the two triangles have the same leg length, which is necessary for HL.

The other options do not directly contribute to proving the triangles are congruent by HL:

"Point P is the midpoint of MK" does not directly provide information about the equality of hypotenuses or legs needed for HL.
"Line MK is the perpendicular bisector of LN" does not directly help with the required congruences.
"ML ≅ MP" is not directly relevant since ML is not a leg of both triangles.

Thus, the two pieces of information that would help in proving ΔLMP ≅ ΔNMP by HL are:

PK ≅ PK
ML ≅ MN