# Study sets matching "geometry postulates"

Ruler Postulate

Segment Addition Postulate (SAP)

Protractor Postulate

Angle Addition Postulate (AAP)

1. The points on a line can be paired with the real numbers in…

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

1. OA is paired with 0, and OB with 180... 2. If OP is paired wit…

If point B lies in the interior of <AOC , then m<AOB + m<BOC =…

Ruler Postulate

1. The points on a line can be paired with the real numbers in…

Segment Addition Postulate (SAP)

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

Line postulate

2 line postulate

Plane postulate

3 point postulate

Through any 2 points there can only be 1 line

If 2 lines intersect, then they intersect in exactly 1 point

If 2 planes intersect, then they intersect in exactly 1 line

Through any 3 noncollinear points there is exactly 1 plane

Line postulate

Through any 2 points there can only be 1 line

2 line postulate

If 2 lines intersect, then they intersect in exactly 1 point

Postulate 1

Postulate 2

Postulate 3

Postulate 4

"The ruler postulate" measure the distance between any two poi…

"Segment Addition postulate" you can add two adjacent (right n…

"Protractor postulate" two places where the angle intersects t…

"Angle addition postulate" you can add two adjacent (right nex…

Postulate 1

"The ruler postulate" measure the distance between any two poi…

Postulate 2

"Segment Addition postulate" you can add two adjacent (right n…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 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

Postulate 2.1

Through any two points, there is exactly one line

Postulate 2.2

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

Postulate

Purpose of a Postulate

Unique-Line-Assumption

Three Ways to Name Unique Lines

Assumptions, a statement assumed to be true, also called an Ax…

To explain undefined terms. To serve as a starting point for l…

Through any two points there is ONE line

1) cursive l ... 2) AB... 3) BA

Postulate

Assumptions, a statement assumed to be true, also called an Ax…

Purpose of a Postulate

To explain undefined terms. To serve as a starting point for l…

2.1 through any two points, there is ex…

2.2 through any three noncollinear poin…

2.3 a line contains at least 2 points

2.4 a plane contains at least 3 noncoll…

line n is the only line through points P and R

plane K is the only plane through noncollinear points A, B, an…

line n contains points A, and B

plane K contains noncollinear points A, B, C, and E

2.1 through any two points, there is ex…

line n is the only line through points P and R

2.2 through any three noncollinear poin…

plane K is the only plane through noncollinear points A, B, an…

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 exact…

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 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

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 pla…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

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

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line

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

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

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 lines intersect, then they intersect in exactly one poi…

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

Two Point Postulate

Line-Point Postulate

Line Intersection Postulate

Three Point Postulate

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 on…

Two Point Postulate

Through any two points there exists exactly one line

Line-Point Postulate

A line contains at least two points

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

through any two points there is exactly one line

through any three noncollinear points there is exactly one pla…

any line contains at least two points

any plane contains at least three noncollinear points

Postulate 2.1

through any two points there is exactly one line

Postulate 2.2

through any three noncollinear points there is exactly one pla…

1

2

3

4

Through any two points there is exactly one line

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

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

Through any three non collinear points there is exactly one pl…

1

Through any two points there is exactly one line

2

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

Segment Addition Postulate

Angle Addition Postulate

Corresponding Angles Postulate

Converse of the Corresponding Angles Po…

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

If S is in the Interior of angle PQR, then the measure of PQS…

If two parallel lines are cut by a transversal, then the pairs…

If two coplanar lines are cut by a transversal so that a pair…

Segment Addition Postulate

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

Angle Addition Postulate

If S is in the Interior of angle PQR, then the measure of PQS…

Segment addition postulate

Through any two points there is exactly…

If two planes intersect then their inte…

through any three points there is at le…

this is an example of what postulate?

Segment addition postulate

this is an example of what postulate?

Through any two points there is exactly…

Two Point Postulate

Line intersection postulate

Three point postulate

Plane line postulate

Through any two points there exists exactly one line

If two lines intersect then there intersection is exactly 1 po…

Through any three noncollinear points there exists exactly 1 p…

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

Two Point Postulate

Through any two points there exists exactly one line

Line intersection postulate

If two lines intersect then there intersection is exactly 1 po…

Postulate Definition

Postulate (Ch 1)

Postulate (Ch 1)

Postulate (Ch 1)

A statement accepted true without proof

The intersection of two lines is a point

The intersection of two planes is a line

Through any two points there is exactly one line

Postulate Definition

A statement accepted true without proof

Postulate (Ch 1)

The intersection of two lines is a point

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with real numbe…

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

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

If P is in the interior of <RST, then m<RSP = m<RSP + m<PST.

Ruler Postulate

The points on a line can be matched one to one with real numbe…

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

line, plane

the points on a line can be paired with real numbers

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

one ray of an angle can be paired with 0 degrees and its oppos…

a ________ contains at least two points, a _______ contains at…

Ruler Postulate

the points on a line can be paired with real numbers

Segment Addition Postulate

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

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 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.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

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

Through any 2 points there is exactly o…

Through any 3 points NOT on the same li…

A line contains at least 2...

A plane contains at least 3 points...

Line

There is exactly one plane

Points

Not on the same line

Through any 2 points there is exactly o…

Line

Through any 3 points NOT on the same li…

There is exactly one plane

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

A quantity is equal to itself... a=a

An equality may be expressed in either order... If a=b, then b=a

Quantities equal to the same quantity are equal to each other.…

A quantity may be substituted for its equal and statement of e…

Reflexive Property of Equality

A quantity is equal to itself... a=a

Symmetric Property of Equality

An equality may be expressed in either order... If a=b, then b=a

Postulate

Angle Addition Postulate (AAP)

Segment Addition Postulate (SAP)

Postulate 5

A basic assumption accepted without proof

...

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

A line contains at least 3 points... A plane contains at least 3…

Postulate

A basic assumption accepted without proof

Angle Addition Postulate (AAP)

...