# Study sets matching "geometry postulates"

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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…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate: Points on a line that match the real numbers.…

Segment Addition Postulate: If B is between A and C, then AB +…

Protractor Postulate: We can number and measure angles.

Angle Addition Postulate: If two angles share a vertex, you ca…

Postulate 1

Ruler Postulate: Points on a line that match the real numbers.…

Postulate 2

Segment Addition Postulate: If B is between A and C, then AB +…

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider OB and a point A on one side of OB. The rays ⃗... of the…

If P is in the interior of ∠RST, then the measure of ∠RST is e…

Ruler Postulate

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

Segment Addition Postulate

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

P 1

P 2

P 3

P 4

Only one straight line can be drawn through two points; two po…

A straight line is the shortest line connecting two points in…

A line segment can be bisected at only one point

Two lines in the same plane either intersect or are parallel.…

P 1

Only one straight line can be drawn through two points; two po…

P 2

A straight line is the shortest line connecting two points in…

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

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…

Number of Points Postulate (Lines)

Number of Points Postulate (Planes)

Number of Points Postulate (Space)

One Line Postulate

A line contains at least 2 points

A plane contains at least 3 points which are not on the same l…

Space contains at least 4 points not on the same plane

Through any two points there is exactly one line

Number of Points Postulate (Lines)

A line contains at least 2 points

Number of Points Postulate (Planes)

A plane contains at least 3 points which are not on the same l…

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

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

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

Three

Two

Line

One Line

A plane contains at least _____________ points, not on the sam…

A line contains at least ______________ points.

If two planes intersect, then their intersection is a ________…

Through any two points there is exactly __________ ___________…

Three

A plane contains at least _____________ points, not on the sam…

Two

A line contains at least ______________ points.

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

a line contains at least two points

through any two points

If ABC then AB + AC = AC, ABC are collinear

If B is inside <AOC then m<AOB + m<BOC = m<AOC

a plane contains at least 3 noncollinear points, space contain…

there is exactly one line

segment addition postulate

If ABC then AB + AC = AC, ABC are collinear

angle addition postulate

If B is inside <AOC then m<AOB + m<BOC = m<AOC

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Only 1 straight line can be drawn through 2 points; 2 points d…

A straight line is the shortest line connecting 2 points on a…

A line segment can be bisected at only 1 point.

2 lines in the same plane either intersect or are parallel. If…

Postulate 1

Only 1 straight line can be drawn through 2 points; 2 points d…

Postulate 2

A straight line is the shortest line connecting 2 points on a…

Postulate

Postulate

Postulate

Segment Addition Postulate

Any two points are collinear

Any three non collinear points are coplanar

If two lines intersect they are coplanar

If L lies between D and Z, the DL+LZ=DZ

Postulate

Any two points are collinear

Postulate

Any three non collinear points are coplanar

2.1

2.2

2.3

2.4

Through any two points, there is exactly one line

Through any three points not on the same line there is exactly…

A line contains at least two points

Plane contains at least three points not on the same line

2.1

Through any two points, there is exactly one line

2.2

Through any three points not on the same line there is exactly…

7

postulate

infinite

one

How many postulates are there?

a statement that is assumed true without proof

a line, plane, and space contain an _____________ number of po…

if there are two points, then exactly ______ line(s) contain(s…

7

How many postulates are there?

postulate

a statement that is assumed true without proof

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

Reflexive Property

Symmetric Property

Transitive Property

Number Line

The same backwards and forwards

The points equal each other no matter the order because its on…

Leave out the middleman

a+b over 2

Reflexive Property

The same backwards and forwards

Symmetric Property

The points equal each other no matter the order because its on…

Three collinear points always lie in ex…

Two lines intersect in exactly one poin…

Through any two points there is exactly…

Through any three non-collinear points…

Never.... One line can lie in infinitely many planes.

Sometimes.... They can also be parallel or not on the same plane.

One.... Two points can form a line.

One.... Three non-collinear points can form a plane, that's why a…

Three collinear points always lie in ex…

Never.... One line can lie in infinitely many planes.

Two lines intersect in exactly one poin…

Sometimes.... They can also be parallel or not on the same plane.

1-1-1

1-1-2

1-1-3

1-1-4

Through any two points there is exactly one line.

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

If two points lie in a plane, then the 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 non collinear points there is exactly one pl…

Postulate #1

Postulate #2

Postulate #3

Postulate #4

To draw a straight line from any point to any point

To produce a finite straight line continuously in a straight l…

To describe a circle with any center and distance

That all right angles are equal to one another

Postulate #1

To draw a straight line from any point to any point

Postulate #2

To produce a finite straight line continuously in a straight l…

Additio property of equality

Subtraction Property of Equality

Multiplication Property of Equality

Division property of equality

If a = b, then a + c = b + c.

If a = b, then a-c = b - c

If a = b, then ac = bc

If a = b and c ≠ 0, then a/c = b/c

Additio property of equality

If a = b, then a + c = b + c.

Subtraction Property of Equality

If a = b, then a-c = b - c