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GEOMETRY POSTULATES – A COMPLETE LIST
P1:
The points on a line can be matched one to one with the
. The
real number that corresponds to a point is the coordinate of the point. The distance
between points A and B , written as
P2:
, is the absolute value of the difference
between the coordinates of A and B ( D  x1  x2 ).
RULER POSTULATE (pg 9)
If B is between A and C , then AB  BC 
.
A
C
B
If AB  BC  AC , then B is
.
SEGMENT ADDITION POSTULATE (pg 10)
P3:
Consider OB and a point A on one side of OB . The rays of the form OA can be matched
one to one with the real numbers from
. The measure of AOB
to
( mAOB ) is equal to the absolute value of the difference between the real numbers for
OA and OB . PROTRACTOR POSTULATE (pg 24)
P4:
R
If P is in the interior of RST ,
P
then mRST 
.
S
ANGLE ADDITION POSTULATE (pg 25)
T
P5:
Through any two points there exists
. (pg 96)
P6:
A line contains at least
. (pg 96)
P7:
If two lines intersect, then their intersection is
. (pg 96)
P8:
Through any three noncollinear points their exists
P9:
A plane contains at least
.
. (pg 96)
P10: If two points lie in a plane, then the line containing them
. (pg 96)
P11: If two planes intersect, then their intersection is a
P12: If two angles form a linear pair, then they are
. (pg 96)
.
LINEAR PAIR POSTULATE (pg 126)
P13: If there is a line and a point not on the line, then there is exactly one line through the
point
to the given line. PARALLEL POSTULATE (pg 148)
P14: If there is a line and a point not on the line, then there is exactly one line through the
point
to the given line. PERPENDICULAR POSTULATE (pg 148)
P15: If two parallel lines are cut by a transversal, then pairs of
are
. CORRESPONDING ANGLES POSTULATE (pg 154)
P16: If two lines are cut by a transversal so the corresponding angels are
then the lines are
. CORRESPONDING ANGLES CONVERSE (pg 161)
P17: In a coordinate plane, two nonvertical lines are parallel if and only if they have
. Any two vertical lines are
to
each other. SLOPES OF PARALLEL LINES (pg 172)
P18: In a coordinate plane, two nonvertical lines are perpendicular if and only if the product
of their slopes is
. Horizontal lines are
to vertical lines.
SLOPES OF PERPENDICULAR LINES (pg 172)
P18 (ALTERNATIVE): In a coordinate plane, two nonvertical lines are perpendicular if and
only if their slopes are
.
P19: If three sides of one triangle are
to three sides of a second
triangle, then the two triangles
.
SIDE-SIDE-SIDE (SSS) CONGRUENCE POSTULATE (pg 234)
P20: If two sides and the included angle of one triangle are
to two sides
and the included angle of a second triangle, then the two triangles
. SIDE-ANGLE-SIDE (SAS) CONGRUENCE POSTULATE (pg 240)
P21: If two angles and the included side of one triangle are
to two angles
and the included side of a second triangle, then the two triangles
. ANGLE-SIDE-ANGLE (ASA) CONGRUENCE POSTULATE (pg 249)
P22: If two angles of one triangle are
to two angels of another triangle,
then the two triangles
.
ANGLE-ANGLE (AA) SIMILARITY POSTULATE (pg 381)
P23: The measure of an arc formed by two adjacent arcs is the
the
of the measures of
. ARC ADDITION POSTULATE (pg 660)
P24: The area of a square is the
AREA OF A SQUARE POSTULATE (pg 720)
of the length of its side, or A 
.
P25: If two polygons are congruent, then they have the same
.
AREA CONGRUENCE POSTULATE (pg 720)
P26: The area of a region is the sum of the areas of all its
. AREA ADDITION POSTULATE (pg 720)
P27: The volume of a cube is the
of the length of its side, or V 
.
VOLUME OF A CUBE POSTULATE (pg 819)
P28: If two polyhedra are congruent, then they have the same
VOLUME CONGRUENCE POSTULATE (pg 819)
P29: The volume of a solid is the sum of the volumes of all its
. VOLUME ADDITION POSTULATE (pg 819)
.