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Lesson Plan: Circles and Triangles Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify inscribed angles in semicircles and circumcircles of triangles and find the equation of a circle given three points on the circumference.
Objectives
Students will be able to
- understand that the inscribed angle in a semicircle is always a right angle,
- find the equation of a circle given three points on the circumference by showing that the three points form a right triangle,
- understand that a unique circle called a circumcircle (or circumscribed circle) can be drawn through the vertices of any triangle,
- find the center of a circle by finding the intersection of the perpendicular bisectors of two chords of the circle,
- find the equation of a circle given three points on the circumference.
Prerequisites
Students should already be familiar with
- equations of circles,
- finding the perpendicular bisector of a line segment.
Exclusions
Students will not cover
- calculating angles of triangles (other than right angles).
