Given: N is the midpoint of line MP, Q is the midpoint of line RP, and line PQ is approximately or equal to line NM. Prove line PN is approximately of equal to line NM

There seems to be extraneous information included (and we look at lengths of segments, not lines - be careful geometry must be precisely written). By definition of midpoint the segment MN and PN are congruent. It seems that this question is either mis-stated, or a "trick question". Please repost if you need to :)