1 / 15

Understanding Arcs, Sectors, and Chords: Geometry Lesson Overview

Today's geometry lesson focuses on arcs, sectors, and their properties as outlined in Chapter 12. We will greet students, review previous assignments, and dive into Lessons 2 and 3, where we explore the concepts of major and minor arcs, the relationship between chords and arcs, and arc addition. Homework will include exercises from the textbook aimed at reinforcing these concepts. The session will conclude with a discussion on how to calculate the area of a sector and important reminders for classroom clean-up.

cynara
Télécharger la présentation

Understanding Arcs, Sectors, and Chords: Geometry Lesson Overview

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. 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!

More Related