1 / 24

Geometry

Geometry. Arcs and Chords. Goals. Identify arcs & chords in circles Compute arc measures and angle measures. Central Angle. An angle whose vertex is the center of a circle. A. Minor Arc. Part of a circle. The measure of the central angle is less than 180 . C. T. A. Semicircle.

dante-stuart
Download Presentation

Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Arcs and Chords

  2. Goals • Identify arcs & chords in circles • Compute arc measures and angle measures

  3. Central Angle An angle whose vertex is the center of a circle. A

  4. Minor Arc Part of a circle. The measure of the central angle is less than 180. C T A

  5. Semicircle Half of a circle. The endpoints of the arc are the endpoints of a diameter. The central angle measures 180. C A T D

  6. Major Arc Part of a circle. The measure of the central angle is greater than 180. C T A D

  7. Major Arc C BUT NOT T A D

  8. Measuring Arcs • An arc has the same measure as the central angle. • We say, “a central angle subtends an arc of equal measure”. A 42 42 B C Central Angle Demo

  9. A 42 42 B C Measuring Major Arcs • The measure of an major arc is given by 360 measure of minor arc. D

  10. R A C T Arc Addition Postulate Postulate Demonstration

  11. Q 40 R T 60 S P 120 What have you learned so far? • Page 607 • Do problems 3 – 8. • Answers… • 3) • 4) • 5) • 6) • 7) • 8)

  12. Chord AB subtends AB. Chord BC subtends BC. Subtending Chords A B O C

  13. Arc Theorems

  14. Theorem 12.4 • Two minor arcs are congruent if and only if corresponding chords are congruent.

  15. Theorem 12.4 B A C D

  16. Example Solve for x. (5x + 10) 120 5x + 10 = 120 5x = 110 x = 22

  17. Theorem 12.5 • If a diameter is perpendicular to a chord, then it bisects the chord and the subtended arc.

  18. Example Solve for x. 52 2x = 52 x = 26 2x

  19. Theorem 12.6 • If a chord is the perpendicular bisector of another chord, then it is a diameter. Diameter

  20. Theorem 12.7 • Two chords are congruent if and only if they are equidistant from the center of a circle.

  21. The red wires are the same length because they are the same distance from the center of the grate.

  22. Example Solve for x. 16 4x – 2 = 16 4x = 18 x = 18/4 x = 4.5 4x – 2

  23. Summary • Chords in circles subtend major and minor arcs. • Arcs have the same measure as their central angles. • Congruent chords subtend congruent arcs and are equidistant from the center. • If a diameter is perpendicular to a chord, then it bisects it.

  24. Practice Problems

More Related