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.