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Lesson Plan: Parallel Chords and Tangents in a Circle Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the parallel chords and the parallel tangents and chords of a circle to deduce the equal measures of the arcs between them and find missing lengths or angles.

Objectives

Students will be able to

  • understand that the measures of the arcs between parallel chords of a circle are equal,
  • understand that the measures of the arcs between a chord and a parallel tangent of a circle are equal,
  • understand that if the measures of the arcs between two chords (or between a chord and a tangent) are equal, we can deduce that the lines must be parallel,
  • use theories of parallel chords and parallel chords and tangents to find unknown angles and lengths.

Prerequisites

Students should already be familiar with

  • chords and tangents of a circle,
  • the Pythagorean theorem,
  • the central angle theorem and arc measures,
  • the relationship between equal arcs and chords.

Exclusions

Students will not cover

  • the equation of a line (in any form),
  • the equation of a circle.

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