1 / 11

Chapter 7 Lesson 6

Chapter 7 Lesson 6. Objective: To find the measures of central angles and arcs. Central Angles and Arcs. In a plane, a circle is the set of all points. The set of all points equidistant from a given point is the center .

linore
Download Presentation

Chapter 7 Lesson 6

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. Chapter 7 Lesson 6 Objective: To find the measures of central angles and arcs.

  2. Central Angles and Arcs • In a plane, a circle is the set of all points. • The set of all points equidistant from a given point is the center. • A radius is a segment that has one endpoint at the center and the other endpoint on the circle. • A diameter is a segment that contains the center of a circle and has both endpoints on the circle.

  3. Congruent Circles have congruent radii. 5 m 5 m Central Angle is an angle whose vertex is the center of the circle. A D C B

  4. Example 1 Finding Central Angles **Remember a circle measures 360°.** Sleep: 31% of 360 .31•360=111.6 Food: 9% of 360 .09•360=32.4 Work: 20% of 360 .20•360=72 Must Do: 7% of 360 .07•360=25.2 Entertainment: 18% of 360 .18•360=64.8 Other: 15% of 360 .15•360=54

  5. An arc is a part of a circle. • Types of arcs • Semicircle is half of a circle. • A DAE Minor arc Major arc AB ADB • A minor arc is smaller than a semicircle. • A major arc is greater than a semicircle. • D

  6. Identify the following in O.   C A • O E D Example 2:Identifying Arcs • the minor arcs • the semicircles • 3. the major arcs that contain point A

  7. Example 3:Identifying Arcs Identify the minor arcs, major arcs and semicircles in O with point A as an endpoint.   • D • A • • minor arcs • AD, AE O • • B E • major arcs • ADE, AED • semicircles • ADB, AEB

  8. Adjacent arcs are arcs of the same circle that have exactly one point in common. Postulate 7-1: Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. mABC = mAB + mBC • • C B • A

  9. Example 4:Finding the Measures of Arcs Find the measure of each arc. • BC 58° D C • BD B 32° • O • ABC A • AB ABC is a semicircle.

  10. Example 5:Finding the Measures of Arcs Find mXY and mDXM in C. M mXY = mXD + mDY mXY = 40 + 56 = 96 Y W C 56° mDXM = mDX + 180 D 40° mDXM = 40 + 180 X mDXM = 220

  11. Assignment pg.389-392 #1-26

More Related