1) The document discusses properties of real numbers related to equality and applying them to measure segments between points on a line. 2) It defines betweenness for three collinear points and shows examples of using subtraction to find distances between points given two point distances. 3) The key properties of equality for real numbers discussed are reflexive, symmetric, transitive, addition/subtraction, multiplication/division, and substitution.

1. Segments and Properties of Real Numbers You will learn to apply the properties of real numbers to the measure of segments. What You'll Learn 1) Betweenness 2) Equation 3) Measurement 4) Unit of Measure 5) Precision Vocabulary

2. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points.

3. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between

4. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. Definition of Betweenness P Q R

5. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between PR + RQ = Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. Definition of Betweenness P Q R PR RQ

6. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between PR + RQ = PQ Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. Definition of Betweenness P Q R PQ

7. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between PR + RQ = PQ NOTE: If and only if (iff) means that both the statement and its converse are true. Statements that include this phrase are called biconditionals . Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. Definition of Betweenness P Q R

8. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

9. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. a = a Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

10. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. a = a if a = b, Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

11. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. a = a if a = b, then b = a Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

12. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. a = a if a = b, then b = a if a = b and b = c Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

13. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. a = a if a = b, then b = a if a = b and b = c then a = c Properties of Equality for Real Numbers . For any number a, Reflexive Property For any numbers a and b, Symmetric Property For any numbers a, b, and c, Transitive Property

14. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. Properties of Equality for Real Numbers . For any numbers a, b, and c, if a = b , Addition and Subtraction Properties For any numbers a, b, and c, if a = b , Multiplication and Division Properties For any numbers a and b, if a = b , Substitution Properties

15. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. then a + c = b + c and a – c = b – c Properties of Equality for Real Numbers . For any numbers a, b, and c, if a = b , Addition and Subtraction Properties For any numbers a, b, and c, if a = b , Multiplication and Division Properties For any numbers a and b, if a = b , Substitution Properties

16. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. then a + c = b + c and then a * c = b * c and a – c = b – c Properties of Equality for Real Numbers . For any numbers a, b, and c, if a = b , Addition and Subtraction Properties For any numbers a, b, and c, if a = b , Multiplication and Division Properties For any numbers a and b, if a = b , Substitution Properties

17. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. then a + c = b + c and then a * c = b * c and a ÷ c = b ÷ c a – c = b – c Properties of Equality for Real Numbers . For any numbers a, b, and c, if a = b , Addition and Subtraction Properties For any numbers a, b, and c, if a = b , Multiplication and Division Properties For any numbers a and b, if a = b , Substitution Properties

18. Segments and Properties of Real Numbers Segment measures are real numbers. Let’s review some of the properties of real numbers relating to EQUALITY. then a + c = b + c and then a * c = b * c and a ÷ c = b ÷ c then a may be replaced by b in any equation. a – c = b – c Properties of Equality for Real Numbers . For any numbers a, b, and c, if a = b , Addition and Subtraction Properties For any numbers a, b, and c, if a = b , Multiplication and Division Properties For any numbers a and b, if a = b , Substitution Properties

19. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. P Q S T

20. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. QS + ST = QT P Q S T

21. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. QS + ST = QT QS + ST – QS = QT – QS P Q S T

22. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. QS + ST = QT QS + ST – QS = QT – QS ST = QT – QS P Q S T

23. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. QS + ST = QT QS + ST – QS = QT – QS ST = QT – QS ST = 52 – 29 = 23 P Q S T

24. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. S P Q T R

25. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. PR + RT = PT S P Q T R

26. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. PR + RT = PT PR + RT – PR = PT – PR S P Q T R

27. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. PR + RT = PT PR + RT – PR = PT – PR RT = PT – PR S P Q T R

28. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. PR + RT = PT PR + RT – PR = PT – PR RT = PT – PR RT = 73 – 27 = 46 S P Q T R

29. End of Lesson Segments and Properties of Real Numbers