# 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.