So I submitted this (with the attatched picture...) but I was told I was missing a few steps.... so I have inputted in purple what I think I may have missed, but I am confused as to the reasoning, or if I'm even on the right track.... thank you for your help!
The line connecting the midpoints of two sides of a triangle is parallel to the third side and is equal to half its length.
STATEMENTS REASONING Points J,L,M form a triangle Given
K is the midpoint of JL Given
N is the midpoint of JM Given
Segment JK is congruent to segment KL Definition of midpoint
Segment JN is congruent to segment NM Definition of midpoint
Segment KN is parallel to segment LM JK/KL = JN/NM à proportional lengths
occur in transversals and parallel lines
Segment LM is congruent to segment JM ?
Segment JM is congruent to segment JL ?
Angles J, L, and M are all equivalent ?
Triangles JKN, KLO, MNO, KNO are all Triangle congruence by
congruent side-angle-side
Segment KN is congruent to segment LO Corresponding parts of
congruent triangles
are congruent (CPCTC)
Segment LO is congruent to segment OM Corresponding parts of
congruent triangles are congruent (CPCTC)
Segment KN is = ½(segment LM) Transitive property of equality