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Lesson Plan: Inscribed Angles Subtended by the Same Arc Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the measures of inscribed angles subtended by the same arc or by congruent arcs.

Objectives

Students will be able to

  • identify that all inscribed angles subtended by the same arc in a circle are equal in measure and calculate the measures of unknown angles, including by solving linear equations,
  • identify that all inscribed angles subtended by congruent arcs in a circle are equal in measure and calculate the measures of unknown angles, including by solving linear equations,
  • identify when the measures of the inscribed angles in distinct circles are equal, in the following two cases:
    • inscribed angles subtended by congruent arcs in congruent circles,
    • inscribed angles subtended by arcs of equal measures in different circles,
    and then find the measures of unknown angles or solve linear equations,
  • recognize that if there are inscribed angles of equal measure in the same circle or in congruent circles, then these angles are subtended by arcs that are equal in measure,
  • recognize that if there are two congruent angles subtended by the same line segment and on the same side of it, then their vertices and the segment’s endpoints lie on a circle in which that segment is a chord.

Prerequisites

Students should already be familiar with

  • central angles and the measures of arcs,
  • inscribed angles and central angles subtended by the same arc or by congruent arcs,
  • parallel chords that subtend congruent arcs in a circle,
  • the main property of a tangent of a circle (that it makes a right angle with the radius or diameter),
  • solving linear equations.

Exclusions

Students will not cover

  • cyclic quadrilaterals,
  • properties of common tangents to a circle.

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