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.