Parallel and Perpendicular Lines


You will continue to develop your ability to write proofs as you focus on the key postulates, theorems, and constructions related to parallel and perpendicular lines. You will also review how to determine distances, midpoints, and slopes, and the equations of lines containing segments. Constructions continue to be introduced, and the ability to combine constructions will become more important. Finally, two lessons are dedicated to worldview issues, including the Geometry in History section.

What you can expect to learn

After completing these activities you should be able to

  1. Identify transversals and related angles formed by a transversal of two lines.
  2. Prove and apply properties of angles formed by a transversal of two parallel lines.
  3. Prove lines parallel using angles related to transversals.
  4. Prove relationships between parallel and perpendicular lines.
  5. Construct a line parallel or perpendicular to a given line.
  6. Combine constructions to construct angles with a given measure.
  7. Find the length and midpoint of a segment in the coordinate plane.
  8. Find the slope of a line in the coordinate plane.
  9. Use the slopes of lines to identify parallel and perpendicular lines.
  10. Graph a line given its equation.
  11. Write an equation of a line given information about its graph.
  12. Identify Descartes’s major contribution to mathematics and evaluate his worldview.
Activity List