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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

Postulate 1: the ruler postulate

Postulate 2: the segment addition post…

Postulate 3

Postulate 4

The real number that corresponds to a point is the coordinate…

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

Protractor Postulate

Angle Addition Postulate

Postulate 1: the ruler postulate

The real number that corresponds to a point is the coordinate…

Postulate 2: the segment addition post…

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

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

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

1-1

1-2

1-3

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…

1-1

Through any two points there is exactly one line

1-2

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

Postulate 1: Ruler Postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

Given any 2 points, exactly one straight line can be drawn th…

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

Given line AB and a point O on line AB, all rays that can be…

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

Postulate 1: Ruler Postulate

Given any 2 points, exactly one straight line can be drawn th…

Segment addition postulate

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

Angle addition postulate

ASA Congruence Postulate

Right Angles are congruent Theorem

Converse of the interior supplements t…

If point D lies in the interior of <ABC, then m<ABD + m<DBC =…

If two angles and the included side and the included side in…

Al right angles are congruent

If two lines are cut by a transversal forming interior angles…

Angle addition postulate

If point D lies in the interior of <ABC, then m<ABD + m<DBC =…

ASA Congruence Postulate

If two angles and the included side and the included side in…

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.

1 Ruler Postulate

2 Segment Addition Postulate

3 Protractor Postulate

4 Angle Addition Postulate

-the distance between two points is absolute value of the dif…

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

-the measure of an angle is the absolute value of the differe…

-if point P is the interior of angle:ABC, then the measure of…

1 Ruler Postulate

-the distance between two points is absolute value of the dif…

2 Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on any line can be paired with real numbers such t…

If Q is between P and R, then PQ+QR=PR.

Given ray AB and a number, R, that's between 0 and 180, there…

If point R is in the interior of angle PQS, then the measure…

Ruler Postulate

The points on any line can be paired with real numbers such t…

Segment Addition Postulate

If Q is between P and R, then PQ+QR=PR.

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, they have exactly one point.

If two distinct planes intersect, they have exactly one line.

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, they have exactly one point.

postulate 1-2

postulate 1-3

postulate 1-1

postulate 1-4

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

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

through any two points there is exactly one line

through any 3 noncollinear points there is exactly one plane

postulate 1-2

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

postulate 1-3

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

Postulates 1-1

Postulates 1-2

Postulates 1-3

Postulates 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…

Postulates 1-1

Through any two points there is exactly one line

Postulates 1-2

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

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…

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Perpendicular to Parallel Theorem

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

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

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

If two lines in the same plane are perpendicular to a third l…

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

postulate 1-1

postulate 1-2

postulate 1-3

postulate 1-4

Through any two points, there is exactly 1 line.

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

If two distint planes intersect then they intersect at exactl…

Through any three noncollinear points there is exactly one pl…

postulate 1-1

Through any two points, there is exactly 1 line.

postulate 1-2

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

Postulate 1

Segment addition postulate

Protractor Postulate

Angle Addition postulate

What can be paired with real numbers to etablish coordinate s…

AB+BC=AC

This is similar to the ruler postulate; if you have a pair of…

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

Postulate 1

What can be paired with real numbers to etablish coordinate s…

Segment addition postulate

AB+BC=AC

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

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

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

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

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

Postulate 1 (Ruler Postulate)

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

Postulate 2 (Segment Addition Postulate)

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

Postulate

Ruler postulate

Segment addition postulate

Protractor postulate

A statement that is accepted as true without proof

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

If B is between A and C, then AB 1 BC 5 AC. If AB 1 BC 5 AC,…

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

Postulate

A statement that is accepted as true without proof

Ruler postulate

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

Postulate 1 (Ruler Postulate)

Postule 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

1. The points on a line can be paried 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 <AOC, then m<AOB + m<BOC =…

Postulate 1 (Ruler Postulate)

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

Postule 2 (Segment Addition Postulate)

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

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

Through any two points there is exactly one line.

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

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

If two lines intersect, then they intersect at exactly one po…

Postulate 1-1-1

Through any two points there is exactly one line.

Postulate 1-1-2

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

Law of Syllogism

Law of Detachment

Postulate 5

Postulate 6

If hypothesis p, then conclusion q.... If hypothesis q, then con…

If the hypothesis of a true statement is true, then ... the conc…

Through any two points there exists exactly one line.

A line contains at least two points.

Law of Syllogism

If hypothesis p, then conclusion q.... If hypothesis q, then con…

Law of Detachment

If the hypothesis of a true statement is true, then ... the conc…

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 exact…

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…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two parts there is exactly one line

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

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

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

Through any two parts there is exactly one line

Postulate 1-2

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

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 nonconllinear points there is exactly one p…

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…

through any ____ points there is exact…

through any three ________ points, the…

a line contains at least __ points.

a plane contains at least ___ noncolli…

two, line

noncollinear, plane

2

3

through any ____ points there is exact…

two, line

through any three ________ points, the…

noncollinear, plane

corresponding angles postulate

alternate interior angles theorem

alternate exterior angles theorem

consecutive interior angles theorem

if 2 parallel limes are cut by a transversal, then EACH PAIR…

if 2 parallel lines are cut by a transversal, then EACH PAIR…

If 2 parallel lines are cut by a transversal, then EACH PAIR…

If 2 parallel lines are cut by a transversal, then EACH PAIR…

corresponding angles postulate

if 2 parallel limes are cut by a transversal, then EACH PAIR…

alternate interior angles theorem

if 2 parallel lines are cut by a transversal, then EACH PAIR…

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

Protractor 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

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

On line AB in a given plane, choose any point 0 between A and…

Ruler Postulate

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

Segment Addition Postulate

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

If B is between A and C... (segment addit…

If B lies interior of <AOC... (angle addi…

Through any 2 points

Through any 3 noncollinear points

then AB+BC=AC

m<AOB+m<BOC=m<AOC

there is exactly 1 line

there is exactly 1 plane

If B is between A and C... (segment addit…

then AB+BC=AC

If B lies interior of <AOC... (angle addi…

m<AOB+m<BOC=m<AOC

Ruler Postulate

Segment Addition Postulate

Linear Pair Postulate

Parallel Postulate

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

What postulate does this rule reflect?... If B is between A and…

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

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

Ruler Postulate

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

Segment Addition Postulate

What postulate does this rule reflect?... If B is between A and…

Angle Addition Postulate

Segment Addition Postulate

Linear Pair Postulate

Parallel Postulate

If point B lies in the interior of ∠AOC then m∠AOB+m∠BOC=m∠AOC

If three points A, B, and C are collinear and B is between A…

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

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

Angle Addition Postulate

If point B lies in the interior of ∠AOC then m∠AOB+m∠BOC=m∠AOC

Segment Addition Postulate

If three points A, B, and C are collinear and B is between A…

There is one line that runs through po…

Line CD contains at least points C and D

Point M is at the intersection between…

Noncollinear points F, G, and H form p…

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…

There is one line that runs through po…

Through any two points there exists exactly one line.

Line CD contains at least points C and D

A line contains at least two points.

Corresponding Angles Converse

Alternate Interior Angles Converse

Alternative Exterior Angles Converse

Consecutive Interior Angles converse

If two lines are cut by a transversal so the corresponding an…

If two lines are cut by a transversal so the alternate interi…

if two lines are cut by a transversal so the alternate exteri…

If two lines are cut by a transversal so the consecutive inte…

Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding an…

Alternate Interior Angles Converse

If two lines are cut by a transversal so the alternate interi…

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

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…

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°

postulate or axiom

Postulate 1.1

Postulate 1.2

Postulate 1.3

an accepted statement of fact

Through any two points, there is exactly one line

If 2 lines intersect, they intersect at exactly one point

If 2 planes intersect, they intersect at exactly one line

postulate or axiom

an accepted statement of fact

Postulate 1.1

Through any two points, there is exactly one line

Postulate 1

Postulate 2

Postulate 3

Postulate 4

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

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.…

Postulate 1

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

Postulate 2

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

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint & Bisector

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

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

A bisector bisects a line segment at its midpoint which divid…

A ray that divides an angle into two adjacent angles that are…

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

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

RULER POSTULATE

SEGMENT ADDITION POSTULATE

PROTRACTOR POSTULATE

ANGLE ADDITION POSTULATE

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

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

Consider RayOB and a point A on one side of RayOB. The rays o…

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

RULER POSTULATE

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

SEGMENT ADDITION POSTULATE

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

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

any segment or angle is congruent/equal to itself (AB = AB) (…

have equal measure

If AB + BC = AC and AB=BC

segment addition postulate

AB + BC = AC

reflexive property

any segment or angle is congruent/equal to itself (AB = AB) (…

Postulate 1... Ruler postulate

Postulate 2... Segment addition postulate

Postulate 3... Protractor postulate

Postulate 4... Angle addition postulate

The points on one line can be matched exactly to real numbers…

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

We haven't learned it yet

If you place two angles side-by-side then the measure of the…

Postulate 1... Ruler postulate

The points on one line can be matched exactly to real numbers…

Postulate 2... Segment addition postulate

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

Addition postulate

Subtraction postulate

Reflexive postulate

Partition postulate

If equal quantities are added to equal quantities, the sums a…

If equal quantities are subtracted from equal quantities, the…

A quantity is congruent (equal) to itself.

The whole is equal to the sum of its parts

Addition postulate

If equal quantities are added to equal quantities, the sums a…

Subtraction postulate

If equal quantities are subtracted from equal quantities, the…