Lesson Plan: Circles Mathematics • 11th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the properties of a circle and its parts in order to solve problems.

Objectives

Students will be able to

  • recall the definition of a circle and the different parts of a circle,
  • understand that all circles are similar,
  • understand the condition required for the congruence of two circles (same radius/diameter),
  • understand that any line passing through the center of a circle is a line of reflectional symmetry,
  • understand basic relationships between the parts of a circle, such as
    • the diameter is twice the radius,
    • the diameter passes through the center of a circle,
    • a chord divides a circle into a major and minor segment,
  • understand that any two radii of a circle and the chord that connects them form an isosceles triangle,
  • understand that if chords of the same length connect radii in the same circle (or in congruent circles), then the two isosceles triangles formed are congruent,
  • use the basic relationships between the parts of a circle and triangles to find unknown angles or lengths.

Prerequisites

Students should already be familiar with

  • similarity and congruence,
  • semicircles and quarter circles,
  • solving linear equations,
  • the Pythagorean theorem,
  • definitions of the following parts of a circle:
    • center,
    • radius,
    • diameter,
    • circumference,
    • chord,
    • tangent,
    • arc,
    • sector,
    • minor segment,
    • major segment.

Exclusions

Students will not cover

  • finding the length of the circumference when given the radius or diameter,
  • finding the area of a circle,
  • the relationship between a radius and a connected tangent (forming a right angle),
  • complex circle theorems (such as the arrowhead, bow tie, and alternate segment theorems),
  • theorems involving equal chords or parallel chords,
  • theorems related to cyclic polygons.

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