Parallel Line Construction

Paper and pencil construction

1. Draw points Q and R on m. Draw line PQ.

2. Draw an arc with the compass point at Q so that it crosses rays QP and QR



3. Copy angle PQR on line QP as shown below. Be sure the two angles are corresponding. Label the new angle TPS as shown below.

4. Draw line PS. Because angle TPS and angle PQR are congruent corresponding angles PS is parallel to line QR.