David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Constructing A Parallel Line
Our goal will be to draw a line through the blue point and parallel to the line through the red and green points.

  1. Find the midpoint of the green and blue points.
  2. Draw a line through the midpoint and the red point.
  3. Draw a circle centered at the midpoint passing through the red point.
  4. Find both points of intersection of the line and circle you just constructed. One of these points will be the red point. The other point of intersection will now be used to construct our line.
  5. Draw a line that passes through the blue point and this "other" point of intersection.
We have now constructed a line through the blue point parallel to the line through the red and green points. Can you prove that the above construction does indeed produce such a line? Move the blue, red and green points around to see how our construction changes.