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Arcs & Chords

Arcs & Chords. Notes 26- Section 10.3 . Essential Learnings. Students will understand and be able to recognize and use relationships between arcs, chords, and diameters. Students will understand and be able to determine radian measures of angles. Vocabulary.

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Arcs & Chords

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  1. Arcs & Chords Notes 26- Section 10.3

  2. Essential Learnings • Students will understand and be able to recognize and use relationships between arcs, chords, and diameters. • Students will understand and be able to determine radian measures of angles.

  3. Vocabulary • Chord – a segment with endpoints on the circle.

  4. Theorem 10.2 • In the same circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

  5. Arc Congruency • In the same circle or congruent circles, if corresponding chords are congruent, then their corresponding arcs and the central angles are congruent.

  6. Example 1 • Find the value of x.

  7. Example 2 • Find the value of x.

  8. Example 3 • Find the value of x.

  9. Theorem 10.3 • If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc.

  10. Theorem 10.4 • The perpendicular bisector of a chord is a diameter of the circle.

  11. Example 4 • In P, the radius 13, RS = 24 and arc RS = 170°. Find each measure. Round to the nearest hundredth. a) RT b) PT

  12. Example 4 cont. • In P, the radius 13, RS = 24 and arc RS = 170°. Find each measure. Round to the nearest hundredth. c) TQ d) arc QS

  13. Theorem 10.5 • In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

  14. Example 5 • In circle P, EF = GH = 24. Find PQ.

  15. Assignment p.705: 7-15 (odd), 16-19, 22, 23, 31-33, 41, 45-50 Quiz – Monday!

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