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Students review some properties of real numbers and apply them to line segments.
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Segments and Properties of Real NumbersSegments 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 NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
between
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
between
Definition
of
Betweenness
Point R is between points P and Q if and only if R, P, and Q arecollinear and _______________.
P QR
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
between
Definition
of
Betweenness
Point R is between points P and Q if and only if R, P, and Q arecollinear and _______________.
P QR
PR + RQ =
PR RQ
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
between
Definition
of
Betweenness
Point R is between points P and Q if and only if R, P, and Q arecollinear and _______________.
P QR
PR + RQ = PQ
PQ
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
Given three collinear points on a line, one point is always _______ the othertwo points.
between
Definition
of
Betweenness
Point R is between points P and Q if and only if R, P, and Q arecollinear and _______________.
P QR
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.
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
Transitive PropertyFor any numbers a, b, and c,
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
Transitive PropertyFor any numbers a, b, and c,
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
if a = b,
Transitive PropertyFor any numbers a, b, and c,
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
if a = b, then b = a
Transitive PropertyFor any numbers a, b, and c,
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
if a = b, then b = a
Transitive PropertyFor any numbers a, b, and c,
if a = b and b = c
Segments and Properties of Real NumbersSegments 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 PropertyFor any numbers a and b,
if a = b, then b = a
Transitive PropertyFor any numbers a, b, and c,
if a = b and b = c then a = c
Segments and Properties of Real NumbersSegments 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
For any numbers a, b, and c, if a = b,
Multiplication andDivision
Properties
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 NumbersSegments 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
For any numbers a, b, and c, if a = b,
then a + c = b + c and
Multiplication andDivision
Properties
For any numbers a, b, and c, if a = b,
Substitution Properties
For any numbers a and b, if a = b,
a – c = b – c
Segments and Properties of Real NumbersSegments 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
For any numbers a, b, and c, if a = b,
then a + c = b + c and
Multiplication andDivision
Properties
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,
a – c = b – c
Segments and Properties of Real NumbersSegments 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
For any numbers a, b, and c, if a = b,
then a + c = b + c and
Multiplication andDivision
Properties
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,
a – c = b – c
Segments and Properties of Real NumbersSegments 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
For any numbers a, b, and c, if a = b,
then a + c = b + c and
Multiplication andDivision
Properties
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.
a – c = b – c
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q S T
If QS = 29 and QT = 52, find ST.
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q S T
If QS = 29 and QT = 52, find ST.
QS + ST = QT
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q S T
If QS = 29 and QT = 52, find ST.
QS + ST = QT
QS + ST – QS = QT – QS
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q S T
If QS = 29 and QT = 52, find ST.
QS + ST = QT
QS + ST – QS = QT – QS
ST = QT – QS
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q S T
If QS = 29 and QT = 52, find ST.
QS + ST = QT
QS + ST – QS = QT – QS
ST = QT – QS
ST = 52 – 29 = 23
S
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q T
If PR = 27 and PT = 73, find RT.
R
S
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q T
If PR = 27 and PT = 73, find RT.
PR + RT = PT
R
S
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q T
If PR = 27 and PT = 73, find RT.
PR + RT = PT
PR + RT – PR = PT – PR
R
S
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q T
If PR = 27 and PT = 73, find RT.
PR + RT = PT
PR + RT – PR = PT – PR
R
RT = PT – PR
S
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
P Q T
If PR = 27 and PT = 73, find RT.
PR + RT = PT
PR + RT – PR = PT – PR
R
RT = PT – PR
RT = 73 – 27 = 46
Segments and Properties of Real NumbersSegments and Properties of Real Numbers
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