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Exploring Chord Properties and Central Angles in Circles

This lesson focuses on the relationships between chords and central angles in circles. Key principles include congruent chords determining congruent central angles and arcs, as well as perpendicular bisectors. Students will learn that the perpendicular from the center of a circle to a chord bisects the chord and is related to distances from the center. The lesson includes problems requiring the calculation of angles and lengths based on given arc measures. This foundational understanding is essential for solving more complex geometric problems.

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Exploring Chord Properties and Central Angles in Circles

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  1. Lesson 7.2

  2. Geometer’s Sketchpad

  3. C-61 If two chords in a circle are congruent, then they determine two central angles that are congruent.

  4. C-62 If two chords in a circle are congruent, then their intercepted arcs are congruent.

  5. C-63 The perpendicular from the center of a circle to a chord is the perpendicular bisector of the chord.

  6. C-64 Two congruent chords in a circle are equally distant from the center of the circle.

  7. C-65 The perpendicular bisector of a chord passes through the center of the circle.

  8. If arc AB = 145o , find the value of angle x. O A x B 145o

  9. Find the value of x

  10. Find the value of x.

  11. If AB = 10 cm, find the length of AM.

  12. If arc AB = 215o , find the value of angle x. A O x 215o B

  13. Homework7.2p. 3351-6, 10-13, 16, 17

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