1 / 45

Lesson 2.4 Curves and Circles pp. 54-59

Lesson 2.4 Curves and Circles pp. 54-59. Objectives: 1. To define a triangle and related terms. 2. To classify curves. 3. To define a circle and related terms. 4. To state the Jordan Curve Theorem. Definition.

annona
Download Presentation

Lesson 2.4 Curves and Circles pp. 54-59

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. Lesson 2.4 Curves and Circlespp. 54-59

  2. Objectives: 1. To define a triangle and related terms. 2. To classify curves. 3. To define a circle and related terms. 4. To state the Jordan Curve Theorem.

  3. Definition A triangle is the union of segments that connect three noncollinear points. A triangle is designated by the symbol  followed by the three noncollinear points.

  4. Triangle R T S Denoted: RST

  5. R T RT RS ST S Triangle opposite sides

  6. Definition A closed curve is a curve that begins and ends at the same point.

  7. Definition A simple curve is a curve that does not intersect itself (unless the starting and ending points coincide).

  8. Definition A simple closed curve is a simple curve that is also a closed curve.

  9. Definition A circle is the set of all points that are a given distance from a given point in a given plane. The center of the circle is the given point in the plane.

  10. O

  11. Definition A radius of a circle is a segment that connects a point on the circle with the center. (The plural of radius is radii.) A chord of a circle is a segment having both endpoints on the circle.

  12. A O

  13. B C O

  14. Definition A diameter is a chord that passes through the center of the circle. An arc is a curve that is a subset of a circle. (symbol: )

  15. B C A O AE D E

  16. Definition The interior of a circle is the set of all planar points whose distance from the center of the circle is less than the length of the radius (r).

  17. O

  18. Definition The exterior of a circle is the set of all planar points whose distance from the center of the circle is greater than the length of the radius (r).

  19. O

  20. Theorem 2.1 Jordan Curve Theorem. Any simple closed curve divides a plane into three disjoint sets: the curve itself, its interior, and its exterior.

  21. Definition A region is the union of a simple closed curve and its interior. The curve is the boundary of the region.

  22. Homework pp. 58-59

  23. ►A. Exercises Classify each figure as (1) a curve, (2) a closed curve, (3) a simple curve, (4) a simple closed curve, (5) or not a curve. Use the most specific term possible. 11.

  24. ►A. Exercises Classify each figure as (1) a curve, (2) a closed curve, (3) a simple curve, (4) a simple closed curve, (5) or not a curve. Use the most specific term possible. 13.

  25. ►A. Exercises Classify each figure as (1) a curve, (2) a closed curve, (3) a simple curve, (4) a simple closed curve, (5) or not a curve. Use the most specific term possible. 15.

  26. ►A. Exercises Classify each figure as (1) a curve, (2) a closed curve, (3) a simple curve, (4) a simple closed curve, (5) or not a curve. Use the most specific term possible. 17.

  27. A B C D E ►B. Exercises Use the figure for exercises 18-22. 19. Name all the angles.

  28. A B C D E ►B. Exercises Use the figure for exercises 18-22. 21. ABD  ADE

  29. ►B. Exercises 23. If X, Y, and Z are noncollinear, find XY  YZ  XZ.

  30. ►B. Exercises Use the figure shown for exercises 25-29. S is the region bounded by rectangle AHFC. Tell whether the statements is true or false. A B C D I H G F E 25. BCI S = BCF

  31. ►B. Exercises Use the figure shown for exercises 25-29. S is the region bounded by rectangle AHFC. Tell whether the statements is true or false. A B C D I H G F E 27. S BGED = BGFC

  32. 29. ABGH BGFC = ACFH  BG ►B. Exercises Use the figure shown for exercises 25-29. S is the region bounded by rectangle AHFC. Tell whether the statements is true or false. A B C D I H G F E

  33. ■ Cumulative Review True/False 32. The intersection of two planes can be a single point.

  34. ■ Cumulative Review True/False 33. The intersection of two opposite half- planes is their common edge.

  35. ■ Cumulative Review True/False 34. A segment is a curve.

  36. ■ Cumulative Review True/False 35. The Line Separation Postulate asserts that a line separates a plane into three disjoint sets.

  37. ■ Cumulative Review True/False 36. If planes s and t are parallel, then every line in plane s is parallel to every line in plane t.

  38. Analytic Geometry Graphing Lines and Curves

  39. Graph y = x + 2 x y

  40. Graph y = -x2 x y

  41. Graph y = x x y

  42. 1. Graph y = x - 5 x y 0 -5 1 -4 2 -3 5 0

  43. 2. Graph y = 3x x y 0 0 1 3 -1 -3

  44. 3. Graph y = x2 + 1 x y 0 1 1 2 -1 2 2 5 -2 5

  45. 4. Graph y = 2x + 3 x y

More Related