# Study sets matching "geometry postulates"

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Addition Postulate

Subtraction Postulate

multiplication postulate

Division Postulate

If equals are added to equals, the sums are equal.

if equals are subtracted from equals, the sums are equal.

doubles of equals are equal.

Halves of equals are equal.

Addition Postulate

If equals are added to equals, the sums are equal.

Subtraction Postulate

if equals are subtracted from equals, the sums are equal.

two, one

two

two, one

three, one

through any _______ points there exists exactly _______ line

a line contains at least ___________ points

if _______ lines intersect, then their intersection is exactly…

through any ___________ noncollinear points there is exists ex…

two, one

through any _______ points there exists exactly _______ line

two

a line contains at least ___________ points

ruler postulate

Segment Addition Postulate (Seg. Add. P…

Protractor Postulate

Angle Addition Postulate

1.)points must be put on a number line... 2.)the distance between…

if B is between A and C, then AB+BC=AC (page 12 in book)

used to find the measure of an angle... 1.) take the absolute val…

m<AOB + m<BOC = m< AOC

ruler postulate

1.)points must be put on a number line... 2.)the distance between…

Segment Addition Postulate (Seg. Add. P…

if B is between A and C, then AB+BC=AC (page 12 in book)

Reflexive Property

transitive property

symmetric property

addition property

A quantity is equal to itself

if two quantities are equal to the same quantity, then they ar…

if a quantity is equal to a second quantity, then the second q…

if equal quantities are added to equal quantities, then the su…

Reflexive Property

A quantity is equal to itself

transitive property

if two quantities are equal to the same quantity, then they ar…

Plane Intersection Postulate

Line Intersection Postulate

Line Point Postulate

Plane Line Postulate

If two planes intersect, then their intersection is a line

If two lines intersect, then their intersection is exactly one…

A line contains at least two points

If two points lie on a plane, then the line containing them li…

Plane Intersection Postulate

If two planes intersect, then their intersection is a line

Line Intersection Postulate

If two lines intersect, then their intersection is exactly one…

Postulate

Point Postulate

Line Postulate

Plane Postulate

Accepted statement of fact

Through any two points there is exactly one line

If two lines intersect, they intersect at exactly one point

If two planes intersect, they intersect it exactly one line

Postulate

Accepted statement of fact

Point Postulate

Through any two points there is exactly one line

1-1-1

1-1-2

1-1-3

1-1-4

Through any two points there is exactly one line

through any three noncollinear point there is exactly one plan…

If two points lie in a plane than that line containing those p…

if two lines intersect, then they intersect in exactly one poi…

1-1-1

Through any two points there is exactly one line

1-1-2

through any three noncollinear point there is exactly one plan…

Supplementary Angles

Complementary Angles

Linear Pair

Vertical Angles

Angles that add to 180 degrees.... m<1+m<2=180

Two angles whose sum is 90 degrees.... m<1+m<2=90

A pair of adjacent angles whose noncommon sides are opposite r…

A pair of opposite congruent angles formed by intersecting lin…

Supplementary Angles

Angles that add to 180 degrees.... m<1+m<2=180

Complementary Angles

Two angles whose sum is 90 degrees.... m<1+m<2=90

P1: Ruler Postulate

P2: Segment Addition Postulate

P3: Protractor Postulate

P4: The Angle Addition Postulate

The points on a line can be paired in a one-to-one corresponde…

If B is between A and C, then AB + BC = AC

Given a point X on (line)PR, consider rays XP and XR, as well…

If point D is in the interior of (angle)ABC, then ... m(angle)ABD…

P1: Ruler Postulate

The points on a line can be paired in a one-to-one corresponde…

P2: Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

through any two points, there exists exactly one line

through any three noncollinear points there exists exactly one…

if two points lie in a plane, then the line containing them li…

if two lines intersect, then their intersection is exactly one…

Postulate 1-1

through any two points, there exists exactly one line

Postulate 1-2

through any three noncollinear points there exists exactly one…

Postulate 1-1 (Postulate: lines and poi…

Postulate 1-2 (Postulate: lines)

Postulate 1-3 (Postulate planes)

Postulate 1-4 (Postulate: points and pl…

Through any two points, there is exactly one line

If two lines intersect, then they intersect in exactly one poi…

If two planes intersect, then they intersect in exactly one li…

Through any three noncollinear points, there is exactly one pl…

Postulate 1-1 (Postulate: lines and poi…

Through any two points, there is exactly one line

Postulate 1-2 (Postulate: lines)

If two lines intersect, then they intersect in exactly one poi…

Ruler Postulate

Segment Addition Postulate

Protractor postulate

Angle Addition Postulate

The point on a line can be matches one to one with the real nu…

If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B is…

Consider line OB and a point A on one side of line OB. The ray…

If P is in the interior so Angle RST then the measure of Angle…

Ruler Postulate

The point on a line can be matches one to one with the real nu…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B is…

Isometry

Transformation

Rigid Motion

Pre-image

A transformation that is rigid

A change in position, size, or shape of a geometric figure

Transformations that preserve distance and angle measure.

The original picture

Isometry

A transformation that is rigid

Transformation

A change in position, size, or shape of a geometric figure

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line.

A line contains at least two points.

If two lines intersect, then their intersection is exactly one…

Through any three noncollinear points there exists exactly one…

Postulate 5

Through any two points there exists exactly one line.

Postulate 6

A line contains at least two points.

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Through any two points there exists exactly one line

If two points lie in a plane then the line that contains them…

Through any 3 non collinear points there exists exactly one pl…

If two distinct lines intersect, then their intersection is ex…

Postulate 1

Through any two points there exists exactly one line

Postulate 2

If two points lie in a plane then the line that contains them…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line

If two distinct lines intersect, then they intersect in exactl…

If two distinct planes intersect , then they intersect in exac…

Through any three noncollinear points there is exactly one pla…

Postulate 1-1

Through any two points there is exactly one line

Postulate 1-2

If two distinct lines intersect, then they intersect in exactl…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line

A line contains at least two points

If two lines intersect, then their intersection is exactly one…

Through any three noncollinear points there exists exactly one…

Postulate 5

Through any two points there exists exactly one line

Postulate 6

A line contains at least two points

a line contains...

a plane contains...

a space contains...

through any 2 points...

...at least 2 points

...at least 2 points, not all on one line

...at least 4 points, not all in one plane

...there is exactly one line

a line contains...

...at least 2 points

a plane contains...

...at least 2 points, not all on one line

2.8(Ruler Postulate)

2.9(Segment Addition Postulate)

2.10(Protractor Postulate)

2.11(Angle Addition Postulate)

The distance between points A and B (AB) is the absolute value…

If B is between A and C then AB+BC=AC

The measure of <AOB is equal to the absolute value of the diff…

If ray P is in the center of <RST then the m<RSP+m<PST=m<RST

2.8(Ruler Postulate)

The distance between points A and B (AB) is the absolute value…

2.9(Segment Addition Postulate)

If B is between A and C then AB+BC=AC

2.1

2.2

2.3

2.4

Through any two points, there is exactly one line

Through any three noncollinear points, there is exactly one pl…

A line contains at least two points

A plane contains at least three noncollinear points

2.1

Through any two points, there is exactly one line

2.2

Through any three noncollinear points, there is exactly one pl…

Parallel Postulate

Corresponding Angles Converse

Alternate Exterior Angles Converse

Alternate Interior Angles Converse

if given a line and a point not on the line, then there exists…

if 2 lines are cut by a transversal so that corresponding angl…

if 2 lines are cut by a transversal so that a pair of alternat…

if 2 lines are cut by transversal so that a pair of alternate…

Parallel Postulate

if given a line and a point not on the line, then there exists…

Corresponding Angles Converse

if 2 lines are cut by a transversal so that corresponding angl…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

through any two points there exists exactly one line

a line contains at least two points

if two lines intersect, then their intersection is exactly one…

through any three non-collinear points there exists exactly on…

Postulate 5

through any two points there exists exactly one line

Postulate 6

a line contains at least two points