1 / 31

Unit 3

Unit 3. Circles & Lines. Section 1. Key Terms. Write down everything you know about circles!. Chord. Line segment that connects two points on a circle Chords equidistant from the center are congruent. Diameter & Radius. Diameter: Chord passing through the center of the circle

emery
Télécharger la présentation

Unit 3

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. Unit 3 Circles & Lines

  2. Section 1 Key Terms

  3. Write down everything you know about circles!

  4. Chord • Line segment that connects two points on a circle • Chords equidistant from the center are congruent

  5. Diameter & Radius • Diameter: Chord passing through the center of the circle • Radius: Line segment from the center to the circumference (outside)

  6. Tangent • Line that touches a circle at exactly one point

  7. Secant • Line that passes through a circle at two points • What’s the difference between a chord, a tangent, and a secant?

  8. Arc • Curve that makes up the circle • Minor Arc: less than 180° • Major Arc: greater than 180° • Semicircle: exactly 180° (half the circle)

  9. Central Angle • Angle whose vertex is on the center of the circle • Measure of a central angle is equal to the measure of the intercepted arc

  10. Example 2

  11. Wrap Up • Exit Slip • Unit 3 Homework Packet

  12. Section 2 Chords

  13. Chords & Arcs • Chords intercepting congruent arcs are congruent • Example: Find the measure of arc AC if arc BA = 150°, and arc BA is congruent to arc CB.

  14. Distance from a Chord to the Center • Example: What is the length of BD? • Hint: What shape do you see in this diagram?

  15. Section 3 Tangents

  16. Tangents • How many tangents can you draw that touch both circles at exactly one point?

  17. Tangents are Perpendicular to the Radius they Intersect • Find the radius. 15 17

  18. Wrap Up • Exit Slip • Homework Packet

  19. Section 4 Arc-Angle Relationships

  20. Inscribed Angle • Angle whose vertex is on the circle • Inscribed angle = Intercepted arc • Example: The measure of arc AC is 80°. Find the measure of AOC and ABC.

  21. Angles Inside the Circle • Angle = ½ (Arc 1 + Arc 2) • Arc BD = 60° and arc AC = 100°. Find the measure of angle AEC. A E D C B

  22. Angles Outside the Circle • Angle = ½ (Arc 1 – Arc 2) • Chord LP is congruent to chord NM. Arc LP measures 130°. Arc LN is three times the measure of arc PM. Find the measure of angle PQM. L P Q M N

  23. Example

  24. Wrap Up • Exit Slip • Homework Packet

  25. Section 5 Segment Product Theorem

  26. Arcs Between Parallel Lines are Congruent • Name the two congruent arcs. A B D C

  27. Segment Product Theorem #1 • LINES, not angles or arcs! • Chord-Chord: AE × EB = CE × ED • Example: Find x. A 9 E 6 3 D C x B

  28. Segment Product Theorem #2 • Tangent-Tangent: CD = AD • “Hat Rule” • Can you prove this?

  29. Segment Product Theorem #3 • Tangent-Secant: PA2 = PB × PC • Example: If PB is 2 inches and BC is 16 inches, find PA.

  30. Segment Product Theorem #4 • Secant-Secant: BE × AE = DE × CE • Example: If AB = 5, CD = 10, and DE = 12, what is the length of BE?

  31. Wrap Up • Exit Slip • Homework Packet Due Friday • Unit 3 Test Friday

More Related