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Exploring Arcs and Angles in Geometry

This program focuses on arcs and angles within circles, inscribed angles, central angles, opposite angles, and parallel secants. Students will investigate various conjectures related to these geometric elements. Source: Discovering Geometry (2008) by Michael Serra and Geometry (2007) by Ron Larson.

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Exploring Arcs and Angles in Geometry

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  1. Arcs and Angles Geometry Regular Program SY 2015-2016 Source: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

  2. Arcs and Angles Conjectures:

  3. Arcs and Angles Given a circle with inscribed angle CAB The inscribed angle and the central angle are intercepting the same arc.

  4. Arcs and Angles Given a circle with inscribed angles P and Q The inscribed angles P and Q are intercepting the same arc.

  5. Arcs and Angles Given a circle with angles inscribed in a semi-circle The inscribed angles intercept a semi-circle.

  6. Arcs and Angles a and c are opposite angles. b and d are opposite angles.

  7. Arcs and Angles Given a circle with two parallel secants Minor Arc AD and Minor Arc BC are in the interior of the two lines

  8. Arcs and Angles Conjectures:

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