Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams

First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a circle to develop relationships. Learners then prove these relationships.

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CCSS: Designed
Instructional Ideas

  • Consider modifying the lesson to extend it to two days, as there are multiple theorems to cover
Classroom Considerations

  • Exploratory challenges require a ruler
  • Proofs require knowledge of similar triangles
  • The 17th installment of a 23-part module
Pros

  • Exploratory challenges keep learners engaged in the subject material
  • Learners develop their own formulas through investigation rather than being told the correct formula
Cons

  • The relationship for secants intersecting exterior to the circle is more commonly expressed using the whole secants and the external segments rather than the internal segments and external segments as in the lesson
Common Core