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Understanding Arcs and Angles in Geometry: Central Angles, Minor and Major Arcs

This section of geometry focuses on arcs and angles, specifically central angles that have the center point as the vertex. Learn how to identify and name minor and major arcs using their endpoints, and understand the relationship between the measure of an arc and the degrees of the central angle that intercepts it. Additional topics include calculating arc lengths and exploring concentric circles with congruent radii. Engage with practical exercises on page 455, problems 19 to 42, to strengthen your understanding of these concepts.

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Understanding Arcs and Angles in Geometry: Central Angles, Minor and Major Arcs

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Presentation Transcript

  1. Geometry Chapter 9 Section 2 Arcs and Angles

  2. Central Angle • An angle with the center point as the vertex

  3. Minor Arc G Minor Arc Name a Minor Arc with its two endpoints J

  4. Major Arc G Major Arc J Name a Major Arc with an endpoint, a point on the circle and another endpoint K

  5. Arc • Measure of an arc = the measure of the degrees of the central angle that intercepts that arc

  6. Angle EWF = 380 Arc EF = 380 Arc EGF = 3600 - 380 F E W J G

  7. Angle EWF = 380 GF is a Diameter Find arc EW Find arc GJE F E W J G

  8. JF = 2(EF) – 5 JG = 2(EF) EG = 2(JG) Find EF F E W J G

  9. Concentric Circles • 2 circles 1 center point

  10. Circles that have congruent radii are congruent circles

  11. Arc Length • The distance of an arc

  12. Find the Arc Length

  13. Find the Arc Length

  14. Find the Arc Length

  15. Find the Arc Length

  16. Do Now • Page 455 problems 19 - 42

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