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Intersection of lines

Intersection of planes

Three non collinear points determine a…

Ruler Postulate

If two distinct lines intersect, they intersect at exactly on…

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

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

Every point of a line can be placed in correspondence with a…

Intersection of lines

If two distinct lines intersect, they intersect at exactly on…

Intersection of planes

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

1.1 Ruler Postulate

1.2 Segment Addition Postulate

1.3 Protractor Postulate

1.4 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.... If AB + BC =AC, t…

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

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

1.1 Ruler Postulate

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

1.2 Segment Addition Postulate

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

through any two points

through any three noncollinear points

on any line

on any plane

there is exactly one line

there is exactly one plane

there are at least two points

there are at least 3 noncollinear points

through any two points

there is exactly one line

through any three noncollinear points

there is exactly one plane

Ruler Postulate (Postulate 1)

Segment Addition Postulate (Postulate 2)

Protractor Postulate (Postulate 3)

Angle Addition Postulate (Postulate 4)

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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.

Ruler Postulate (Postulate 1)

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

Segment Addition Postulate (Postulate 2)

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

AB + BC = AC (part + part = whole)

m∠ABC = m∠ABP + m∠CBP ... (part + part =…

exactly 1 line.

2 points.

P2 - The Segment Addition Postulate... If B is between points A…

P4 - The Angle Addition Postulate... If P is a point interior to…

P5... Through any two points there exists

P6... A line contains at least

AB + BC = AC (part + part = whole)

P2 - The Segment Addition Postulate... If B is between points A…

m∠ABC = m∠ABP + m∠CBP ... (part + part =…

P4 - The Angle Addition Postulate... If P is a point interior to…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

through any two given points there is one line

If two distinct lines intersect, they intersect in exactly on…

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

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

through any two given points there is one line

Postulate 1-2

If two distinct lines intersect, they intersect in exactly on…

Postulate #1

Postulate #2

Postulate #3

Postulate #4

RULER POSTULATE - On a number line, every point can be paired…

SEGMENT ADDITION POSTULATE -

PROTRACTOR POSTULATE -

ANGLE ADDITION POSTULATE -

Postulate #1

RULER POSTULATE - On a number line, every point can be paired…

Postulate #2

SEGMENT ADDITION POSTULATE -

Postulate 1

Postulate 2

The Ruler Postulate

Corollary to Ruler Postulate

Two points determine a line

Three noncollinear points determine a plane

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

A line segment has exactly ONE midpoint

Postulate 1

Two points determine a line

Postulate 2

Three noncollinear points determine a plane

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Two points on a line can be paired with real numbers... (A=0,B=1…

AB+BC=AC

You can pair rays with real #s... (if OP=x and OQ=y then m<POQ=I…

exactly like segment addition postulate

Ruler Postulate

Two points on a line can be paired with real numbers... (A=0,B=1…

Segment Addition Postulate

AB+BC=AC

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Two points determine a unique straight line.

Three noncollinear points determine a unique plane.

The Ruler Postulate: (a) To every point on a line, there corr…

The Protractor Postulate: (a) The rays in a half rotation (18…

Postulate 1

Two points determine a unique straight line.

Postulate 2

Three noncollinear points determine a unique plane.

two point postulate/line point postulate

line intersection postulate

three point postulate

plane point postulate

through any two points there exists exactly one line

if two lines intersect then their intersection is exactly one…

through any three non collinear points there exists exactly o…

a plane contains at least three non collinear points

two point postulate/line point postulate

through any two points there exists exactly one line

line intersection postulate

if two lines intersect then their intersection is exactly one…

1.1 Ruler Postulate

1.2 Segment Addition Postulate

1.3 Protractor Postulate

1.4 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.... If AB + BC =AC, t…

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

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

1.1 Ruler Postulate

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

1.2 Segment Addition Postulate

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

1 Ruler Postulate

2 Segment Addition Postulate

3 Protractor Postulate

4 Angle Addition Postulate

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

When 3 points are collinear, you can say one point is between…

The measurement of a angle between two rays can be designated…

If a point is in the interior of an angle, the measure of the…

1 Ruler Postulate

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

2 Segment Addition Postulate

When 3 points are collinear, you can say one point is between…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any 2 points there is exactly one line

Through any 3 non collinear points there is exactly 1 plane

A line contains at least 2 points

A plane contains at least three non collinear points

Postulate 2.1

Through any 2 points there is exactly one line

Postulate 2.2

Through any 3 non collinear points there is exactly 1 plane

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 Ray Ob. ... The ray…

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

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,…

parallel postulate

perpendicular postulate

translation postulate

reflection postulate

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

If there is a line and a point not on the line, then there is…

a translation is a rigid motion

a reflection is a rigid motion

parallel postulate

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

perpendicular postulate

If there is a line and a point not on the line, then there is…

Segment Addition Postulate

Angle Addition Postulate

Postulate 5

Postulate 6

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

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

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

through any two points, there is exactly one line

Segment Addition Postulate

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

Angle Addition Postulate

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

postulate 5

postulate 6

postulate 7

postulate 8

Through any two points there is exactly one line

A line contains at least 2 points

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

Through any 3 non-collinear points there exist exactly one pl…

postulate 5

Through any two points there is exactly one line

postulate 6

A line contains at least 2 points

Through two distinct points, there is…

The measure of any line segment is a u…

If X is a point of segment AB and A-X-…

If two lines intersect, they intersect…

Postulate 1

Postulate 2: Ruler Postulate

Postulate 3: Segment-Addition Postulate

Postulate 4

Through two distinct points, there is…

Postulate 1

The measure of any line segment is a u…

Postulate 2: Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

Two Point Postulate

Line-Point Postulate

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

If ray B is a segment bisector of ∠ABC, then m∠AOB + m∠BOC =…

Through any two points there exists exactly 1 line

A line contains at least 2 points

Segment Addition Postulate

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

Angle Addition Postulate

If ray B is a segment bisector of ∠ABC, then m∠AOB + m∠BOC =…

Ruler Postulate (Postulate 1)

Segment Addition Postulate (Postulate 2)

Protractor Postulate (Postulate 3)

Angle Addition Postulate (Postulate 4)

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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.

Ruler Postulate (Postulate 1)

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

Segment Addition Postulate (Postulate 2)

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

3.1 Corresponding Angles Postulate

3.2 Slopes of Parallel Lines Postulate

3.3 Slopes of Perpendicular Lines Post…

3.4 Converse of Corresponding Angles P…

if two parallel lines are cut by a transversal, then each pai…

two non vertical lines have the same slope if and only if the…

two non vertical lines are perpendicular if and only if the p…

if two lines are cut by a transversal so that corresponding a…

3.1 Corresponding Angles Postulate

if two parallel lines are cut by a transversal, then each pai…

3.2 Slopes of Parallel Lines Postulate

two non vertical lines have the same slope if and only if the…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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.

xxx Given a point, X, on PR, consider XP and XR, as well as a…

xxx If point D is in the interior of ABC, then m ABD + m DBC…

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

1) Scale- can match points on line with numbers... 2) Distance b…

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

1) Scale... 2) Angle measure

1) If D is in the interior of angle ABC, then the measure of…

Ruler Postulate

1) Scale- can match points on line with numbers... 2) Distance b…

Segment Addition Postulate

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

Postulate

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3: Protractor Postulate

A statement that is accepted as true without proof.

The points on a line can be put into a one-to-one corresponde…

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

The measurement of an angle between two rays can be designate…

Postulate

A statement that is accepted as true without proof.

Postulate 1: Ruler Postulate

The points on a line can be put into a one-to-one corresponde…

Ruler Postulate (Postulate 1)

Segment Addition Postulate (Postulate 2)

Protractor Postulate (Postulate 3)

Angle Addition Postulate (Postulate 4)

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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.

Ruler Postulate (Postulate 1)

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

Segment Addition Postulate (Postulate 2)

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

Addition 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, then a/c = b/c... *c cannot equal 0

Addition Property of Equality

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

Subtraction Property of Equality

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

Postulate 1

Postulate 2

Postulate 3

Postulate 4

points on a line can be matched one to one with real numbers

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

the measure of aoc is equal to the absolute value of the dist…

if b is the interior of coa, then the measure of coa= the mea…

Postulate 1

points on a line can be matched one to one with real numbers

Postulate 2

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

Distance Postulate

Ruler Postulate

Ruler Placement Postulate

The Line Postulate

To every pair of different points there corresponds a unique…

The points of a line can be placed in correspondence with the…

Given two points P and Q of a line, the coordinate system can…

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

Distance Postulate

To every pair of different points there corresponds a unique…

Ruler Postulate

The points of a line can be placed in correspondence with the…

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Postulate

Corresponding Angles Converse

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

If two lines are cut by a transversal so that the correspondi…

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

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

Postulate 1

Postulate 2

Postulate 3

Postulate 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 non collinear points there is exactly one p…

Postulate 1

Through any two points there is exactly one line

Postulate 2

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

Ruler Postulate

Segment Addition Postulate

Distance Formula

Protractor Postulate

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

B is between A and C iff A B + B C = A C

The rays in a half rotation can be numbered from 0 to 180. Th…

Ruler Postulate

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

Segment Addition Postulate

B is between A and C iff A B + B C = A C

1-1-1... Points, Lines, and Planes

1-1-2... Points, Lines, and Planes

1-1-3... Points, Lines, and Planes

1-1-4... Intersection of lines and planes

Through any two points there is exactly one line

Through any three noncollinear points there is exactly one pl…

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

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

1-1-1... Points, Lines, and Planes

Through any two points there is exactly one line

1-1-2... Points, Lines, and Planes

Through any three noncollinear points there is exactly one pl…

through any two points

through any three noncollinear points

if two points lie on a plane

the intersection of two lines

there is exactly one line

there is exactly one plane

then the line containing those points is also on the plane

is exactly one point

through any two points

there is exactly one line

through any three noncollinear points

there is exactly one plane

2.1

2.2

2.3

2.4

Through any 2 points, there is exactly one line

Through any 3 noncollinear points, there is exactly 1 plane

a line contains at least 2 points

a plane contains at least 3 noncollinear points

2.1

Through any 2 points, there is exactly one line

2.2

Through any 3 noncollinear points, there is exactly 1 plane

2.1

2.2

2.3

2.4

Through any two points is exactly one line.

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

A line contains at least two points.

A plane contains at least three non collinear points

2.1

Through any two points is exactly one line.

2.2

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

ruler postulate

protracture postulate

Angle addition postulate

segment addition postulate

Ruler Postulate Summary. On a number line, every point can be…

The Protractor Postulate. Given line AB and a point O on line…

The angle addition postulate states that if B is in the inter…

The segment addition postulate is a fairly obvious-seeming po…

ruler postulate

Ruler Postulate Summary. On a number line, every point can be…

protracture postulate

The Protractor Postulate. Given line AB and a point O on line…

Ruler Postulate

Protractor Postulate

Angle Addition Postulate

Segment Addition Postulate

The ruler postulate tells us how to find the distance between…

Given line AB and a point O on line AB. Consider rays OA and…

The angle addition postulate states that if B is in the inter…

The segment addition postulate is a fairly obvious-seeming po…

Ruler Postulate

The ruler postulate tells us how to find the distance between…

Protractor Postulate

Given line AB and a point O on line AB. Consider rays OA and…

P5

P6

P7

P8

Through only two points,there is exactly one line. ... If you h…

A line contains at least two points. If you have a line, then…

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

Through any three non-collider points, there is exactly one p…

P5

Through only two points,there is exactly one line. ... If you h…

P6

A line contains at least two points. If you have a line, then…

Corresponding angles theorem

Alternate interior angles theorem

Alternate exterior angles

Same side interior angles theorem

If two lines are cut by a transveral then the pairs if corr a…

If parallel then alt int angles congruent

If parallel cut by a transversal then alt ext angles congruent

If parallel same side interior angles supp

Corresponding angles theorem

If two lines are cut by a transveral then the pairs if corr a…

Alternate interior angles theorem

If parallel then alt int angles congruent

postulates

Angle Addition Postulate

Linear Pair Postulate

Segment Addition Postulate

Rules that are accepted without proof

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

If two angles form a linear pair, then they are supplementary

If E is between A and C, then AE + EC = AC

postulates

Rules that are accepted without proof

Angle Addition Postulate

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

Intersection of lines

Intersection of planes

Three non collinear points determine a…

Ruler Postulate

If two distinct lines intersect, they intersect at exactly on…

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

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

Every point of a line can be placed in correspondence with a…

Intersection of lines

If two distinct lines intersect, they intersect at exactly on…

Intersection of planes

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

Addition 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, then a/c = b/c... *c cannot equal 0

Addition Property of Equality

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

Subtraction Property of Equality

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

postulate 1

postulate 2

postulate 3

postulate 4

through any two points there is exactly one line.

through any three non-collinear points there is exactly one p…

a line contains at least two points

a plane contains at least three non-collinear points.

postulate 1

through any two points there is exactly one line.

postulate 2

through any three non-collinear points there is exactly one p…

Intersection of lines

Intersection of planes

Three non collinear points determine a…

Ruler Postulate

If two distinct lines intersect, they intersect at exactly on…

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

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

Every point of a line can be placed in correspondence with a…

Intersection of lines

If two distinct lines intersect, they intersect at exactly on…

Intersection of planes

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