Shortest Line Segment from a Point P to a Line L

This Shortest Line Segment from a Point P to a Line L activity & project also includes:

One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the class develops a distance proof using only the Pythagorean Theorem. This problem makes a great open-ended test question or classroom refresher to keep the level of math rigor high in the classroom.

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CCSS: Designed
Instructional Ideas

  • Suggested modification has pupils develop the diagram from the written description, instead of providing the diagram in the exercise
  • Include as part of a lesson on developing math from fundamental principles and axioms, extending the question to its application in spherical geometry
Classroom Considerations

  • Specifying that only the Pythagorean Theorem is needed would change the emphasis of this problem from solving the actual puzzle to the proper use of fundamental principles

  • Short problem easily incorporated into a number of lessons (Pythagorean Theorem, proof development, constructions, etc.)
  • Straightforward directions and diagram allow focusing on logical development of mathematical argument

  • Class exercise not separated from the teaching notes and answer key
Common Core