Lesson Plan: Proving Cyclic Quadrilaterals Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to prove that a quadrilateral is cyclic using the angles resulting from its diagonals.

Objectives

Students will be able to

  • identify whether a quadrilateral is cyclic from the measures of the angles between its diagonals and sides,
  • prove that a quadrilateral is cyclic by using the measures of the angles between its diagonals and sides.

Prerequisites

Students should already be familiar with

  • the perpendicular bisector of a chord in a circle,
  • the main property of a tangent to a circle (that it makes a right angle with the radius or the diameter),
  • central angles and measures of arcs,
  • the inscribed angle theorems,
  • parallel chords and tangents in a circle,
  • theories of equal chords.

Exclusions

Students will not cover

  • other properties of cyclic quadrilaterals, including supplementary opposite angles, equal exterior angles, and the interior angle at the opposite vertex,
  • properties of common tangents to a circle.

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