Lesson Plan: Relationships Between Chords and The Center of a Circle Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify the relationship between chords that are equal or different in length and the center of a circle and use the properties of the chords in congruent circles to solve problems.

Objectives

Students will be able to

• identify the longer of two chords in a circle based on their distance from the center (and vice versa) and use this theory to solve inequalities,
• prove that two chords of equal lengths in the same circle or in congruent circles are equidistant from the center of the circle and use this theory to find unknown lengths and angles and solve equations,
• recognize that two chords in a circle or in congruent circles are equal in length when they are equidistant from the center(s) and use this theory to find unknown lengths and angles and solve equations.

Prerequisites

Students should already be familiar with

• chords and perpendicular bisectors of chords,
• common chords in intersecting circles.

Exclusions

Students will not cover

• measures of arcs,
• central angles,
• inscribed angles in a circle.