1 / 34

Understanding Chords and Angles in Circles: Geometry Presentation

This PowerPoint presentation explores the relationship between chords, secants, and tangents in circles, focusing on vertical angles and arc measures. It discusses how intersecting chords create vertical angles that are congruent, examines the angles formed by secants with arcs, and explains the relationship between tangent lines and angles. The presentation includes illustrations, angle measurements, and interactive components to enhance understanding of circular geometry concepts. Ideal for students seeking to grasp the fundamental principles of angles and arcs within circles.

quiana
Télécharger la présentation

Understanding Chords and Angles in Circles: Geometry Presentation

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. Other Angle Relationships In Circles Geometry Chapter 10 A BowerPoint Presentation

  2. 2 chords • Draw 2 intersecting chords in your circle • Label a pair of vertical angles as angles 1 and 2 • What do you know about angles 1 and 2?

  3. 2 chords • Draw 2 intersecting chords in your circle • Label a pair of vertical angles as angles 1 and 2 • What do you know about angles 1 and 2? • They are congruent!

  4. 2 chords • Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent?

  5. 2 chords • Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent? • No!

  6. 2 chords

  7. 2 chords

  8. 2 chords • Find the measures of angles 1 & 2

  9. 2 chords • Find the measures of angles 1 & 2 Both angles = 110o

  10. 2 chords • Find x

  11. 2 chords • Find x x = 80

  12. 2 secants • Put a point outside the circle (probably to the right) • Draw two secants that go through that point and through the circle • Do you see how the angle you’ve created intercepts two arcs in the circle?

  13. 2 secants

  14. 2 secants

  15. 2 secants • Find the measure of angle 1

  16. 2 secants • Find the measure of angle 1 Angle 1 = 50o

  17. 2 secants • Find x

  18. 2 secants • Find x x = 130

  19. 1 secant & 1 tangent • Put a point outside the circle (probably to the right) • Draw a secant that goes through the circle and through the point • Draw a tangent that touches the circle at one point and goes through your point • Do you see how the angle you’ve created intercepts two arcs in the circle?

  20. 1 secant & 1 tangent

  21. 1 secant & 1 tangent

  22. 1 tangent & 1 secant • Find the measure of angle 1

  23. 1 tangent & 1 secant • Find the measure of angle 1 Angle 1 = 45o

  24. 1 secant & 1 tangent • Find x

  25. 1 secant & 1 tangent • Find x x = 90

  26. 2 tangents • Put a point outside the circle (probably to the right) • Draw two tangents that each touch the circle once and intersect at your point • Do you see how the angle you’ve created intercepts two arcs in the circle?

  27. 2 tangents

  28. 2 tangents

  29. 2 tangents • Find the measure of angle 1 (There is enough information!)

  30. 2 tangents • Find the measure of angle 1 (There is enough information – how big is green arc?)

  31. 2 tangents • Find the measure of angle 1 Angle 1 = 80o

  32. 2 tangents • Find x

  33. 2 tangents • Find x x– (360 – x)= 2 (50)

  34. 2 tangents • Find x x = 230

More Related