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Midpoint connector theorem

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