Answer:
The additional information necessary is option;
D. [tex]\overline {MN}[/tex] ⊥ [tex]\overline {LP}[/tex]
Step-by-step explanation:
From the given figure, we have;
Given that ML ≅ MP,
The Hypotenuse Leg HL theorem of congruency is used to prove that a given number of right triangles based on the lengths of their hypotenuse and one of the legs. It states that two or more right triangles are congruent if they have equal lengths of both their corresponding hypotenuse side and one leg
To prove that ΔLMN and ΔPMN are congruent by HL, we will also be required to prove that ΔLMN and ΔPMN are right triangles
For ΔLMN and ΔPMN to be right triangles, the angles, ∠LNM and ∠PNM should be right angles = 90°
With ∠LNM = ∠PNM = 90°, then, line [tex]\overline {MN}[/tex] is perpendicular to line [tex]\overline {LP}[/tex] or [tex]\overline {MN}[/tex] ⊥ [tex]\overline {LP}[/tex]
Therefore, the additional information necessary to prove that ΔLMN ≅ ΔPMN by HL is [tex]\overline {MN}[/tex] ⊥ [tex]\overline {LP}[/tex].
