Upcoming SlideShare
×

# Segments and Properties of Real Numbers (Geometry 2_2)

10,782 views

Published on

Students review some properties of real numbers and apply them to line segments.

4 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
10,782
On SlideShare
0
From Embeds
0
Number of Embeds
1,256
Actions
Shares
0
243
0
Likes
4
Embeds 0
No embeds

No notes for slide

### Segments and Properties of Real Numbers (Geometry 2_2)

1. 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. 2. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points.
3. 3. Segments and Properties of Real Numbers Given three collinear points on a line, one point is always _______ the other two points. between
4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. P Q S T
20. 20. Segments and Properties of Real Numbers If QS = 29 and QT = 52, find ST. QS + ST = QT P Q S T
21. 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. 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. 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. 24. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. S P Q T R
25. 25. Segments and Properties of Real Numbers If PR = 27 and PT = 73, find RT. PR + RT = PT S P Q T R
26. 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. 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. 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. 29. End of Lesson Segments and Properties of Real Numbers