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27 Cards in this Set
 Front
 Back
MIDPOINT

a point M is the midpoint of line segment STif and only if M is between S and T and
SM = MT 

postulate 24
COMPLETENESS PROPERTY FOR POINTS IN THE PLANE (FOR GRAPH) 
FOR EACH POINT IN A COORDINATE PLANE CORRESPONDS TO ONLY ONE ORDERED PAIR (X,Y)
OF REAL NUMBERS. AND EACH ORDERED PAIR OF REAL NUMBERS CORRESPONDS TO ONE POINT ON THE COORDINATE PLANE. 

postulate 21
THE NUMBER LINE POSTULATE 
each real number corresponds to one and only one point on the number line. Each point on the number line corresponds to 1 real number!


SYMMETRIC PROPERTY of equality
for real numbers 
for any numbers a and b
if a=b then b=a 9each side looks like a mirror image of the other side) 

REAL numbers

includes RATIONAL and
IRRATIONAL numbers 

postulate 22
DISTANCE POSTULATE 
for any two points on a number line and a given unit of measure, there is a unique positive real number called the MEASURE of distance between the 2 points


THEOREM 26
MIDPOINT FORMULA FOR A COORDINATE PLANE 
x one + x two
 2 and y one + y two ________________ 2 

REFLEXIVE PROPERTY of equality for real numbers

for any number a
then: a=a 

MULTIPLICATION AND DIVISION
PROPERTIES of equality for real numbers 
for any numbers: a, b, and c
if a x c = b x c mult and if c is not equal to zero if a/c = b/c division(can't have 0 in denomin 

congruence of line segments is
symmetric 
SEE PAGE 63


TRANSATIVE PROPERTY of equality for real numbers

for any numbers (can be more than 3) a, b, and c if
a=b and b=c then a=c 

CONGRUENT SEGMENTS

two segments are congruent if and only if they have the same
length 

Congruence of line segments is REFLEXIVE

see pg 63


VECTOR

a DIRECTED line segment if shows movement is a certain direction.
Magnitude=length of vector. arrowhead=direction of vector 

ADDITION AND SUBTRACTION of
equality for real numbers 
for any numbers a, b, and c
if a=b then; a+c=b+c and addition ac=bc subtraction 

postulate 23
RULER POSTULATE 
the points on a line can be pared with the real numbers so that the measure of the distance between corresponding points is the positive (absolute value) distance of the 2 numbers


PRECISION OF MEASUREMENT

depends on the smallest unit of measure being used eg 1/16 in. GREATEST POSSIBE ERROR IS
ONEHALF THE SMALLEST UNIT OF MEASURE (EG 1/2OF 1/16 OR 1/32 INCH) 

congruence of line segments is
TRANSATIVE 
see page 63


MEASUREMENTS

measurements such as 10 inches
are composed of 2 parts 10 (the number of units) inches(the unit of measure) check to include the U of M 

RATIONAL numbers

any number written as a/b
wher a and b are intergers (whole numbers) and b is not zero ************* 

definition of BETWEENNESS

3 COLINNEAR POINTS
IF R IS BETWEEN POINT P AND POINT Q THEN: PR + RQ = PQ 

theorm 25
MIDPOINT FORMULA FOR A NUMBER LINE 
A+B
_________ 2 

IRRATIONAL numbers

decimals that to not end and do not repeat
example 0.66666666 etc or pi 3.141 etc 

THEORM 24

IF a and b are real numbers, a vertical line contains all points (x,y)such that x=a and a horizontal line contains all points (x,y) suth that y=b
the equation of a vertical line is x=a and the equation of a horizontal line is y=b 

COORDINATE of a line

the NUMBER that corresponds to the point (address) on the line


WHOLE numbers

includes zero and the counting numbers


SUBSTITUTION PROPERTY of equality for ral numbers

for any numbers a and b
if a=b then a may be replaced by b in any equation (you can substitute one for the other) 