Segments and Properties of Real Numbers (Geometry 2_2)

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


Given three collinear points on a line, one point is always _______ the othertwo points.



between



between

Definition

of

Betweenness

Point R is between points P and Q if and only if R, P, and Q arecollinear and _______________.

P QR



between

Definition

of

Betweenness


P QR

PR + RQ =

PR RQ



between

Definition

of

Betweenness


P QR

PR + RQ = PQ

PQ



between

Definition

of

Betweenness


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.


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,




Reflexive Property For any number a, a = a








if a = b,







if a = b, then b = a









if a = b and b = c








if a = b and b = c then a = c




Addition and Subtraction Properties

For any numbers a, b, and c, if a = b,

Multiplication andDivision

Properties


Substitution Properties

For any numbers a and b, if a = b,






then a + c = b + c and


Properties




a – c = b – c








Properties


then a * c = b * c and



a – c = b – c








Properties


then a * c = b * c and a ÷ c = b ÷ c



a – c = b – c








Properties


then a * c = b * c and a ÷ c = b ÷ c



then a may be replaced by b in any equation.

a – c = b – c


P Q S T

If QS = 29 and QT = 52, find ST.


P Q S T


QS + ST = QT


P Q S T


QS + ST = QT

QS + ST – QS = QT – QS


P Q S T


QS + ST = QT


ST = QT – QS


P Q S T


QS + ST = QT


ST = QT – QS

ST = 52 – 29 = 23

S


P Q T

If PR = 27 and PT = 73, find RT.

R

S


P Q T


PR + RT = PT

R

S


P Q T


PR + RT = PT

PR + RT – PR = PT – PR

R

S


P Q T


PR + RT = PT


R

RT = PT – PR

S


P Q T


PR + RT = PT


R

RT = PT – PR

RT = 73 – 27 = 46

Segments and Properties of Real Numbers (Geometry 2_2)

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