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Chords and Arcs Geometry 11-2 • Central Angle – An angle where the vertex is the center of the circle • Inscribed Angle – An angle where the vertex is on the arc of the circle and the sides of the angle are chords of the circle Vocabulary • Compass • Protractor Get your supplies 1. Draw a large circle, O 2. Draw two congruent chords ST and AR, use your compass to ensure they are A congruent. 3. Construct lines OS, OT, OA and OR 4. Measure angles AOR and TOS T O S R Chord Exploration If two chords in a circle are congruent, then they determine two central angles that are congruent T A O If two central angles in a circle are congruent, then they determine two arcs that are congruent S R Chord Central Angle Theorem If two chords in a circle are congruent, then their intercepted arcs are congruent T A O S R Chord Arc Theorem Chord Arc Theorem 1. Draw a large circle 2. Add a chord to the circle 3. Construct a perpendicular bisector of the chord – use the compass and the ruler 4. Repeat steps 2 and 3 with a congruent chord 5. What do you notice about the two bisector lines? Chord Exploration The diameter from the center of a circle perpendicular to a chord is the perpendicular bisector of the chord Perpendicular to a Chord Theorem Compare the distance from the center of the circle to each of the congruent chords Chord Exploration Two congruent chords in a circle are equidistant from the center of a circle Chord distance to center Theorem • Construct a perpendicular bisector of the chord – use the compass and the ruler Chord Exploration • Repeat the process again Chord Exploration • What do you notice about the two bisector lines? Chord Exploration • What do you notice about the two bisector lines? This is the center of the circle So what conclusion can we draw about the two bisectors? They are both diameters Chord Exploration The perpendicular bisector of a chord passes through the center of a circle Perpendicular to a chord Theorem Chord Theorems Chord Theorems Sample Problems Practice Problems Practice Problems Practice Problems Practice Problems Practice Problems • Pages 593 – 596 • 4 – 18 even, 26, 30, 48 Homework • Pages 593 – 596 • 4 – 18 even, 26, 30, 39, 48 Honors Homework
