Geometry: Chords of a Circle

Objectives

• Students will explore the relationship between chords of a circle and their perpendicular bisectors.
• Students will discover that the perpendicular bisector of a chord always passes through the center of a circle.
• Students will discover that a line perpendicular to a chord that passes through the center of a circle always bisects the chord. Students then apply these relationships to right triangles.
• Students will discover that two chords are congruent if and only if they are equidistant from the center of a circle.

Vocabulary

• chord of a circle
• perpendicular bisector
• equidistant

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.