Segments and Properties of Real Numbers
You will learn to apply the properties of real numbers to the measure of segments.
1) Betweenness 2) Equation
3) Measurement
4) Unit of Measure
5) Precision
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other two points.
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other between two points.
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other between two points.
Point R is between points P and Q if and only if R, P, and Q are collinear and _______________.
P R
Definition of Betweenness
Q
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other between two points.
Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. PR + RQ =
P R
Definition of Betweenness
Q
PR
RQ
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other between two points.
Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. PR + RQ = PQ
P R
Definition of Betweenness
Q
PQ
Segments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the other between two points.
Point R is between points P and Q if and only if R, P, and Q are collinear and _______________. PR + RQ = PQ
P R
Definition of Betweenness
Q
NOTE: If and only if (iff) means that both the statement and its converse are true. Statements that include this phrase are called biconditionals.
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. Reflexive Property
For any number a,
Symmetric Property
For any numbers a and b,
Transitive Property
For any numbers a, b, and c,
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. Reflexive Property
For any number a,
a=a
Symmetric Property
For any numbers a and b,
Transitive Property
For any numbers a, b, and c,
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. Reflexive Property
For any number a,
a=a
Symmetric Property
For any numbers a and b,
if a = b,
Transitive Property
For any numbers a, b, and c,
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. Reflexive Property
For any number a,
a=a
Symmetric Property
For any numbers a and b,
if a = b, then b = a
Transitive Property
For any numbers a, b, and c,
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. Reflexive Property
For any number a,
a=a
Symmetric Property
For any numbers a and b,
if a = b, then b = a
Transitive Property
For any numbers a, b, and c,
if a = b and b = c
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. Reflexive Property
For any number a,
a=a
Symmetric Property
For any numbers a and b,
if a = b, then b = a
Transitive Property
For any numbers a, b, and c,
if a = b and b = c
then a = c
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. Addition and Subtraction Properties Multiplication and Division Properties
For any numbers a, b, and c, if a = b,
For any numbers a, b, and c, if a = b,
Substitution Properties
For any numbers a and b, if a = b,
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. Addition and Subtraction Properties Multiplication and Division Properties
For any numbers a, b, and c, if a = b,
then a + c = b + c
and a – c = b – c
For any numbers a, b, and c, if a = b,
Substitution Properties
For any numbers a and b, if a = b,
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. Addition and Subtraction Properties Multiplication and Division Properties
For any numbers a, b, and c, if a = b,
then a + c = b + c
and a – c = b – c
For any numbers a, b, and c, if a = b,
then a * c = b * c
and
Substitution Properties
For any numbers a and b, if a = b,
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. Addition and Subtraction Properties Multiplication and Division Properties
For any numbers a, b, and c, if a = b,
then a + c = b + c
and a – c = b – c
For any numbers a, b, and c, if a = b,
then a * c = b * c
and
a÷c=b÷c
Substitution Properties
For any numbers a and b, if a = b,
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. Addition and Subtraction Properties Multiplication and Division Properties
For any numbers a, b, and c, if a = b,
then a + c = b + c
and a – c = b – c
For any numbers a, b, and c, if a = b,
then a * c = b * c
and
a÷c=b÷c
Substitution Properties
For any numbers a and b, if a = b,
then a may be replaced by b in any equation.
Segments and Properties of Real Numbers
If QS = 29 and QT = 52, P Q
find ST. S T
Segments and Properties of Real Numbers
If QS = 29 and QT = 52, P Q
find ST. S T
QS + ST = QT
Segments and Properties of Real Numbers
If QS = 29 and QT = 52, P Q
find ST. S T
QS + ST = QT
QS + ST – QS = QT – QS
Segments and Properties of Real Numbers
If QS = 29 and QT = 52, P Q
find ST. S T
QS + ST = QT
QS + ST – QS = QT – QS ST = QT – QS
Segments and Properties of Real Numbers
If QS = 29 and QT = 52, P Q
find ST. S T
QS + ST = QT
QS + ST – QS = QT – QS ST = QT – QS ST = 52 – 29 = 23
Segments and Properties of Real Numbers
If PR = 27 and PT = 73, P Q
find RT. R S T
Segments and Properties of Real Numbers
If PR = 27 and PT = 73, P Q
find RT. R S T
PR + RT = PT
Segments and Properties of Real Numbers
If PR = 27 and PT = 73, P Q
find RT. R S T
PR + RT = PT
PR + RT – PR = PT – PR
Segments and Properties of Real Numbers
If PR = 27 and PT = 73, P Q
find RT. R S T
PR + RT = PT
PR + RT – PR = PT – PR RT = PT – PR
Segments and Properties of Real Numbers
If PR = 27 and PT = 73, P Q
find RT. R S T
PR + RT = PT
PR + RT – PR = PT – PR RT = PT – PR RT = 73 – 27 = 46
Segments and Properties of Real Numbers