1. Constructing Parallel Lines
Basic Constructions
Constructing Parallel Lines

2. Given a line l and a point P not on l, construct a line through P, parallel to line l.
Step 1: Draw a line that goes through P so that it intersects line l. Label this point A. Q
Next, we need to copy angle A at P. P l
Step 2: Opening your compass to any comfortable position, set your compass at A and make an arc that intersects both sides of the angle. Label these points B and C.
Put compass point here B
Step 3: Using the same opening, set your compass at P and make an identical mark. Where the arc intersects the line from step 1, label that point Q. C A
Put compass point here

3. Given a line l and a point P not on l, construct a line through P, parallel to line l.
Put compass point here
Step 4: Set your compass at B and make an arc that intersects line l at C. P l C A B Q
Step 5: Using the same opening, set your compass at Q and make an arc that intersects the arc from step 3. Label this point R.
Put compass point here R
Step 6: Draw
“If two lines are cut by a transversal so that corresponding angles are congruent, then the two lines are parallel”
Therefore,