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Basic Constructions Constructing Parallel Lines 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 B A 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 C Put compass point here l 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. Given a line l and a point P not on l, construct a line through P, parallel to line l. Put compass point here Q P 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 hereR B A Step 4: Set your compass at B and make an arc that intersects line l at C. Step 6: Draw PR C l “If two lines are cut by a transversal so that corresponding angles are congruent, then the two lines are parallel” Therefore, PR AC