Question 159445
let line AB represent line L
let line CD represent line M
let line EF represent line N
draw vertical line AB perpendicular to horizontal line CD and horizontal line EF.
point A is on the top of line AB and point B is on the bottom.
point C is on the left of line CD and point D is on the right.
point E is on the left of line EF and point F is on the right.
let line AB intersect line CD at K
let line AB intersect line EF at M
since AB is perpendicular to CD at K, then angle AKC is 90 degrees (property of perpendicular lines is that they intersect at right angles).
since angle AKC is equal to 90 degrees, then AKD, CKM, DKM are all equal to 90 degrees (supplementary angles of right angles are right angles).
since AB is perpendicular to EF at M, then angles KME, EMB, KMF, FMB are all right angles for the same reasons quoted for the intersecting angles of AB perpendicular to CD.
alternate interior angles DKM equal to KME (both equal to 90 degrees so equal to each other).
CD is parallel to EF (if alternate interior angles of two lines are congruent then the lines are parallel.  this is a basic postulate of parallel lines).
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these are the steps i believe your proof should take.  you may state or restate in whatever format is required.  proofs are in (...)