1 / 34

Chapter 2

Segment Measure and Coordinate Graphing. Chapter 2. Real Numbers and Number Lines. Section 2-1. NATURAL NUMBERS - set of counting numbers. {1, 2, 3, 4, 5, 6, 7, 8…}. WHOLE NUMBERS – set of counting numbers plus zero. {0, 1, 2, 3, 4, 5, 6, 7, 8…}. INTEGERS –

palani
Download Presentation

Chapter 2

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. Segment Measure and Coordinate Graphing Chapter 2

  2. Real Numbers and Number Lines Section 2-1

  3. NATURAL NUMBERS - set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8…}

  4. WHOLE NUMBERS – set of counting numbers plus zero {0, 1, 2, 3, 4, 5, 6, 7, 8…}

  5. INTEGERS – set of the whole numbers plus their opposites {…, -3, -2, -1, 0, 1, 2, 3, …}

  6. RATIONAL NUMBERS - numbers that can be expressed as a ratio of two integers a and b and includes fractions, repeating decimals, and terminating decimals

  7. EXAMPLES OFRATIONAL NUMBERS 0.375 = 3/8 0.66666…= 2/3 0/5 = 0

  8. IRRATIONAL NUMBERS - numbers that cannot be expressed as a ratio of two integers a and b and can still be designated on a number line

  9. REAL NUMBERS Include both rational and irrational numbers

  10. Coordinate • The number that corresponds to a point on a number line

  11. AbsoluteValue • The number of units a number is from zero on the number line

  12. Segments and Properties of Real Numbers Section 2-2

  13. Betweeness • Refers to collinear points • Point B is between points A and C if A, B, and C are collinear and AB + BC = AC

  14. Example • Three segment measures are given. Determine which point is between the other two. • AB = 12, BC = 47, and AC = 35

  15. Measurement and Unit of Measure • Measurement is composed of the measure and the unit of measure • Measure tells you how many units • Unit of measure tells you what unit you are using

  16. Precision • Depends on the smallest unit of measure being used

  17. Greatest Possible Error • Half of the smallest unit used to make the measurement

  18. Percent Error Greatest Possible Error x 100 measurement

  19. Congruent Segments Section 2-3

  20. Congruent Segments • Two segments are congruent if and only if they have the same length

  21. Theorems • Statements that can be justified by using logical reasoning

  22. Theorem 2-1 • Congruence of segments is reflexive

  23. Theorem 2-2 • Congruence of segments is symmetric

  24. Theorem 2-3 • Congruence of segments is transitive

  25. Midpoint • A point M is the midpoint of a segment ST if and only if M is between S and T and SM = MT

  26. Bisect • To separate something into two congruent parts

  27. The Coordinate Plane Section 2-4

  28. Coordinate Plane • Grid used to locate points • Divided by the y-axis and the x-axis into four quadrants • The intersection of the axes is the origin

  29. An ordered pair of numbers names the coordinate of a point • X-coordinate is first in the ordered pair • Y-coordinate is second in the ordered pair

  30. Postulate 2-4 • Each point in a coordinate plane corresponds to exactly one ordered pair of real numbers. Each ordered pair of real numbers corresponds to exactly one point in a coordinate plane.

  31. Theorem 2-4 • If a and b are real numbers, a vertical line contains all points (x, y) such that x = a, and a horizontal line contains all points (x, y) such that y = b.

  32. Midpoints Section 2-5

  33. Theorem 2-5Midpoint formula for a line • On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinate a and b is a+b. 2

  34. Theorem 2-6Midpoint formula for a Coordinate Plane • On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x1, y1) and (x2, y2) are (x1 + x2 , y1 + y2) 2 2

More Related