Looking More Carefully at Parallel Lines

Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then examine the alternate interior angles. 

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CCSS: Designed
Instructional Ideas

  • Use each example as guided instruction; learners will need guidance with language and notation
Classroom Considerations

  • Time suggestions are provided, but allow extra time if needed to develop the concepts
  • Requires prior experience with constructions and parallel lines cut by a transversal
Pros

  • Mathematically challenging lesson that encourages deep thinking and justifications
  • Teaching guidance is provided that highlights the connections and conclusions pupils should make
Cons

  • Uses a ruler to measure a midpoint during a construction; for a true construction, the midpoint should be found using a compass and straightedge only