Geometry: Cyclic Quadrilaterals

Objectives

• You have seen before that for any triangle, you can find a circle that contains all 3 vertices (called the circumscribed circle or the circumcircle). When the 4 vertices of a quadrilateral lie on a circle, it is a special situation and deserves a special name: cyclic quadrilateral. In this activity, students will investigate some of the properties of cyclic quadrilaterals.

Vocabulary

• circumscribed circle
• perpendicular bisector
• supplementary angles

About the Lesson

This lesson is intended to be introduced by the teacher and completed by the students, as they discover and justify their conjectures. Students might work independently or with a partner to complete this activity. The time varies for this activity depending on whether the TI-Nspire document (.tns file) is given to or created by the students.