In the figure, QN¯¯¯¯¯¯¯¯ is the perpendicular bisector of LM¯¯¯¯¯¯¯¯¯. Which of the following can be used to prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯?

First, state that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ by the definition of a perpendicular bisector. Second, state that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ because of the definition of congruence.

First, state that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent. Second, state that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ because of the definition of congruence.

First, prove that △LNP≅△MNP by the side-side-side theorem. Second, prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ by showing that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent.

First, prove that △LNP≅△MNP by the side-angle-side theorem. Second, prove that point P is equidistant from the endpoints of LM¯¯¯¯¯¯¯¯¯ by showing that PL¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯ because corresponding parts of congruent triangles are congruent.