#### Study sets matching "geometry postulates"

#### Study sets matching "geometry postulates"

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

Postulate 1

Postulate 2

The Ruler Postulate (Postulate 3)

The Protractor Postulate (Postulate 4)

Two points determine a unique straight line.

Three noncollinear points determine a unique plane

a. To every point on a line there corresponds exactly one rea…

a. The rays in a half rotation (180 degrees) can be numbered…

Postulate 1

Two points determine a unique straight line.

Postulate 2

Three noncollinear points determine a unique plane

Postulate 1.2

Postulate 1.3-1 (Two Points Determine…

Postulate 1.3-2 (Intersection of Lines)

Postulate 1.3-3 (Intersection of Planes)

Two points make a line

Two lines intersect at a point

Two planes intersect at a line

Two planes intersect at a line

Postulate 1.2

Two points make a line

Postulate 1.3-1 (Two Points Determine…

Two lines intersect at a 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…

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

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 po…

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

Through any three noncollinear points there is exactly one pl…

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 po…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Through any two points there is exactly one line

If two lines intersect they intersect in exactly one point

If two planes intersect, they intersect in exactly one line

Through any three non-collinear points there exists exactly o…

Postulate 1

Through any two points there is exactly one line

Postulate 2

If two lines intersect they intersect in exactly one point

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

accepted rule that a ruler can find a distance

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

the measure of an angle is equal to the absolute value of the…

if P is in the interior of the angle RST, then the measure of…

Ruler Postulate

accepted rule that a ruler can find a distance

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Given two points, there corresponds a unique positive number…

Given two rays, there corresponds a unique positive number ca…

Ruler Postulate

Given two points, there corresponds a unique positive number…

Segment Addition Postulate

Postulate 1- Ruler Postulate

Postulate 2- Segment Addition Postulate

Postulate 3

Postulate 4- Angle Addition Postulate

the points on a line can be paired with the real numbers in s…

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

rays can be paired with the real numbers from 1-180

if a point lies in the interior of and angle, then you would…

Postulate 1- Ruler Postulate

the points on a line can be paired with the real numbers in s…

Postulate 2- Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

Postulate(a statement that is accepted…

Postulate 2

Postulate 3, postulate 4

Postulate 5

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

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

Please see the text book for diagram explanation

Through any two points there is exactly one line

Postulate(a statement that is accepted…

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

Postulate 2

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

Postulate 1 - Ruler Postulate

Postulate 2 - Segment Addition Postulate

Postulate 3 - Protractor Postulate

Postulate 4 - Angle Addition Postulate

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

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

<AOB is equal to the absolute value of the difference between…

If B is the interior of angle AOC, then the measure of angle…

Postulate 1 - Ruler Postulate

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

Postulate 2 - Segment Addition Postulate

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

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

the points on a line can paired in a one-to-one correspondenc…

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 a…

if point D is in the interior of angle ABC, then m angleABD +…

ruler postulate

the points on a line can paired in a one-to-one correspondenc…

segment addition postulate

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

The Distance Postulate (2-4)

The Ruler Postulate (2-5)

The Ruler Placement Postulate (2-5)

The Line Postulate

To every pair of different points there corresponds a unique…

1. One point of the line for each number... 2. One number for ea…

Given 2 Points of a line, the coordinate system can be shifte…

For every two different points there is exactly one line that…

The Distance Postulate (2-4)

To every pair of different points there corresponds a unique…

The Ruler Postulate (2-5)

1. One point of the line for each number... 2. One number for ea…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

Postulate 1-1 Through any two points,…

Postulate 1-2 If two distinct lines in…

Postulate 1-3 If two distinct _______i…

Postulate 1-4 Through any ________poin…

line

point

planes

three noncollinear

Postulate 1-1 Through any two points,…

line

Postulate 1-2 If two distinct lines in…

point

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

If you take a line segment and divide it into equal segments…

If B is between A and C, then AB + BC = AC (the parts add up…

On line AB in a given plane, chose any point O between A and…

If point B lies in the interior of /_AOC, then the m/_AOB + m…

Ruler Postulate

If you take a line segment and divide it into equal segments…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC (the parts add up…

Side Angle Side (SAS)

Side Side Side (SSS)

Included Angles

Included Sides

If 2 sides and an included angle are congruent to 2 sides and…

Three sides of one triangle are congruent to three sides of t…

Angle formed by 2 adjacent sides

Sides located between 2 angles

Side Angle Side (SAS)

If 2 sides and an included angle are congruent to 2 sides and…

Side Side Side (SSS)

Three sides of one triangle are congruent to three sides of t…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The distance between points A and B, written as AB, is the ab…

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

The measure of angle AOB is equal to the absolute value of th…

If P is the interior of angle RST, then the measure of angle…

Ruler Postulate

The distance between points A and B, written as AB, is the ab…

Segment Addition Postulate

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

points existence postulate

straight line postulate

plane postulate

flat plane postulate

space contains at least four noncoplanar points. every plane…

two points are contained in one and only one line (two points…

three noncollinear points are contained in one and only one p…

if two points are in a plane, then the line containing the po…

points existence postulate

space contains at least four noncoplanar points. every plane…

straight line postulate

two points are contained in one and only one line (two points…

Transitive Postulate

Substitution Postulate

Partition Postulate

Reflexive Postulate

Equal things are equal.... If A=B and C=B, then A=C

A quantity may be substituted for its equal in any expression…

The whole equals the sum of its parts.

Any quantity equals itself.

Transitive Postulate

Equal things are equal.... If A=B and C=B, then A=C

Substitution Postulate

A quantity may be substituted for its equal in any expression…

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

ruler postulate

Segment Addition Postulate (Seg. Add.…

Protractor Postulate

Angle Addition Postulate

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

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 va…

m<AOB + m<BOC = m< AOC

ruler postulate

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

Segment Addition Postulate (Seg. Add.…

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

Postulate 1

Postulate 2

Postulate 3 The Ruler Postulate

Postulate 4 The Protractor Postulate

Two points determine a line.

Three noncollinear points determine a line.

The points on a line can be numbered so that positive number…

The rays in a half-rotation can be numbered from 0 to 180 so…

Postulate 1

Two points determine a line.

Postulate 2

Three noncollinear points determine a line.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be match one to one with real number…

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

Consider a point A on one side of line OB. The rays of a form…

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

Ruler Postulate

The points on a line can be match one to one with real number…

Segment Addition Postulate

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

Same Side Interior Angles Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then the same…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then alternat…

Same Side Interior Angles Postulate

If a transversal intersects two parallel lines, then the same…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

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 on…

Through any three noncollinear 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.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

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 i…

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 wi…

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 i…

Segment Addition Postulate (SAP)

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

Postulate 1

Postulate 2

Postulate 3

Postulate 4

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

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

"Protractor postulate" two places where the angle intersects…

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

Postulate 1

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

Postulate 2

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

Postulate

Purpose of a Postulate

Unique-Line-Assumption

Three Ways to Name Unique Lines

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

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

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 A…

Purpose of a Postulate

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

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 p…

Through any three noncollinear points there exists exactly 1…

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

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 p…

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 po…

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

Through any three noncollinear points there is exactly one pl…

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 po…

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…

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 pl…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any 2 points there is exactly one line.

If 2 distinct lines intersect, then they intersect in exactly…

If two distinct planes intersect, they intersect in exactly o…

Through any non-collinear points there is exactly one plane.

Postulate 1-1

Through any 2 points there is exactly one line.

Postulate 1-2

If 2 distinct lines intersect, then they intersect in exactly…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

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

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

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of angle AOC, then measure of…

Postulate 1 (Ruler Postulate)

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

Postulate 2 (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 is exactly one line.

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

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

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

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

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 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 po…

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

Through any three noncollinear points there is exactly one pl…

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 po…

Through any 2 points there is exactly…

Through any 3 points NOT on the same l…

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…

Line

Through any 3 points NOT on the same l…

There is exactly one plane

1

2

3

4

Through any two points there is exactly one line

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

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

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

1

Through any two points there is exactly one line

2

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

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 c…

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…

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 contai…

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

Three

Two

Line

One Line

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

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 sa…

Two

A line contains at least ______________ points.

segment addition postulate

angle addition postulate

postulate

postulates 1

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

If point B lies in the interior of angle AOC then the measure…

a basic assumption

a line contains at least two points; a plane contains at leas…

segment addition postulate

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

angle addition postulate

If point B lies in the interior of angle AOC then the measure…

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 p…

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

7

How many postulates are there?

postulate

a statement that is assumed true without proof