Question 254420: Draw a horizontal line l and a point P not on l. Construct a line m through P perpendicular to l. Draw a point Q not on m or l. Construct a line n though Q perpendicular to m. What postulate or theorem guarantees that the lines l and n are parallel?
Answer by MRperkins(300)   (Show Source):
You can put this solution on YOUR website! First of all, make sure that you are able to follow instructions and be sure to draw a picture to try and figure this out. If you are doing it in your head, then put what is in your head on paper. I have drawn my illustration and it appears that you have a couple of options. You should look at the beginning of the section that you are dealing with to see which one your book is most likely wanting. In my book, Theorem 3.4.5 says, "If two coplanar lines are perpendicular to the same line, then the two lines are parallel". I believe this is the theorem they are wanting (not the number, just what is in quotes). You could also justify this by the converse of the alt. int. angles theorem, converse of the same side int. angles thm., converse of the alt. ext. angles theorem, or the converse of same side ext. angles thm.
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