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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #81: From Ch. 12, Lesson 2 (pp. 491-496): Set I Exercises 1-3, 15-28. Bonus: Set II Exercises 46-53 and/or Set III. Lesson: Arcs & Sectors Homework / Questions Clean-up. How much cake is in this slice?.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #81: From Ch. 12, Lesson 2 (pp. 491-496): • Set I Exercises 1-3, 15-28. • Bonus: Set II Exercises 46-53 and/or Set III. • Lesson: Arcs & Sectors • Homework / Questions • Clean-up

  3. How much cake is in this slice?

  4. Goals for Today (Ch. 12 Lesson 3) • Know the terms major (or minor) arc,central angle, and measure (of an arc). • Understand & use arc addition. • Relate chords to arcs.

  5. Definitions – Review • An arc is a contiguous portion of a circle. • A minor arc goes less than halfway around. • A major arc goes more than halfway around. • (A semicircle goes exactly halfway.) • A central angle of a circle is an anglewhose vertex is the circle’s center. • A reflex angle has a measure greater than 180°. • Reflex angles correspond to major arcs.

  6. Abbreviations • This would be called “Arc XY”: • Abbreviated: • Use a third letter to distinguish major arcs: • “Major Arc XY through W” • Abbreviated:

  7. Arc Measure • The measure of an arc is the measure of its central angle. • Often abbreviated withan “m” before the arc name:

  8. Arc Measure • The same holds true for major arcs, naturally:

  9. Postulate: Arc Addition

  10. Chords & Arcs • Theorem (61): • In a circle, equal chords have equal arcs. • Proof is given in Lesson 3.

  11. Chords & Arcs • Theorem (62): • In a circle, equal arcs haveequal chords. • Given: In circle O: • Prove: AB = CD • Hints for the proof: • Draw AB & CD. • Draw and use radii. • Use the definition of arc measure.

  12. How much cake is in this slice?

  13. Definitions • The slice is a sector of a circle: • A sector of a circle is aregion bounded by the circleand two of its radii. • A sector’s area is a fraction of the circle’s area. • The fraction is the central angle⁄360°

  14. Homework • Asg #82: From Ch. 12, Lesson 3 (pp. 498-503): • Set I Exercises 1-7, 23-29. • Set II Exercises 40-42. • Bonus: Set II Exercises 44-45. • Due Thursday, 5/30. • Asg #83: From Ch. 14, Lesson 6 (pp. 605-611): • Set I Exercises 1-11, 26-30. • Set II Exercises 31-33. • Bonus: Set II Exercises 57-65. • Due Friday, 5/31. • Unit 11 Test Analysis: Due Monday, 6/3.

  15. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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