1. Segment Measure and Coordinate Graphing

2. Real Numbers and Number Lines

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 OF RATIONAL 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. Absolute Value  The number of units a number is from zero on the number line

12. Segments and Properties of Real Numbers

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

20.  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

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

33. Theorem 2-5 Midpoint 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 2-6 Midpoint formula for a Coordinate Plane  On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1, y 1 ) and (x 2, y 2 ) are (x 1 + x 2, y 1 + y 2 ) 2 2