Two Column Proof: Statement Reasons 1. I is the midpoint of ML D is the midpoint of MN 1. Given 2. Extend ID until E such that ID=DE 2. Construction 3. MD DN 3. 4. MDI NDE 4. Vertical Angle Theorem 5. AMDI - ANDE 5. 6. MI NE 6. 7. MI IL 7. Definition of Midpoint 8. Transitive Property of Segment 8. IL EN Congruence 9. ZIMD ZEND 9. Converse of the Alternate Interior Angles IL EN Theorem 10. Quadrilateral ILNE is a parallelogram 10. 11. Opposite sides of a parallelogram are 11. TEILN parallel 12. TE=ID+DE 12. Definition of Betweenness 13. D+DE=2(D) 13. Substitution from Statement 2 and 12 14. IE=2(ID) 14. Transitive Property 15. IE=LN 15. Opposite sides of a parallelogram are congruent. 16. 2(ID)=LN 16. Substitution from Statement 14 and 15 17.ID = ELNO 17​