Right Triangles Inscribed in Circles II

This Right Triangles Inscribed in Circles II lesson plan also includes:

So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a right angle uses properties of midsegments and similar triangles. The proof using quadrilaterals is also outlined, for interested parties. Leading questions help guide learners through the proof, while still leaving the structure open for development.

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CCSS: Designed
Instructional Ideas

  • Suggested differentiations include amending or removing specific instruction hints
  • Great activity for extending existing skill practice on circle properties, or showing application of triangle characteristics
Classroom Considerations

  • May need some support or review of midsegments and other triangle properties if that lesson is not recent

  • Clear application of triangle properties that can often seem isolated and not useful
  • Excellent open-ended question to help develop mathematical writing and logic skills

  • Student worksheet not separated from teaching notes and answer key
Common Core