Circles, Chords, Diameters, and Their Relationships

A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords and diameters. They then prove provided theorems about chords and diameters.

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CCSS: Designed
Instructional Ideas

  • Keep a running list of theorems for this lesson, as well as subsequent lessons
Classroom Considerations

  • Activity requires compass and straightedge
  • Writing proofs and sharing with the class is likely to take more than the 20 minutes allotted in the lesson
  • The second installment of a 23-part series

  • Problem set includes applications of the theorems to mathematical problems
  • Teacher resource includes all answers to student worksheets, including exit ticket and problem sets

  • Some of the proofs are easier than others, which may provide inequitable learning experiences for different groups
Common Core