You can put this solution on YOUR website! draw horizontal line segment AB to represent line L.
draw horizontal line segment CD underneath AB and parallel to AB representing line M parallel to line L.
draw vertical line segment EF perpendicular to AB and approximately in the middle of it representing line N perpendicular to line L. let EF pass through CD as well representing line N intersecting with line M as well as line L.
call the intersection of AB and EF point G.
call the intersection of CD and EF point H.
you should have:
horizontal line AB.
horizontal line CD parallel to it.
vertical line EF passing through AB at point G, and passing through CD at point H.
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AB perpendicular to EF (given)
angle BGF = 90 degrees (if lines are perpendicular to each other then their angle of intersection equals 90 degrees).
angle CHE = angle BGF (alternate interior angles of parallel lines are equal).
angle CHE = 90 degrees (equal to angle BGF which is 90 degrees)
CD perpendicular to EF (if the angle of intersection equals 90 degrees then the lines forming the angle of intersection are perpendicular to each other).
(