Lesson: Inscribed Angles Subtended by the Same Arc Mathematics

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.