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Ruler Postulate

Segment Addition Postulate

Congruent Figures

Congruent Segments

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

Have the same size and shape

Have equal lengths

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

Midpoint Theorem

Angle Bisector Theorem

Theorem 1-4

Theorem 1-5

if M is the midpoint of segment AB, then: 2AM=AB and AM=(1/2)…

if ray BX is the bisector of angle ABC, then: ... 2m angle ABX=m…

adjacent angles formed by perpendicular lines are congruent

if two lines form congruent adjacent angles, then the lines a…

Midpoint Theorem

if M is the midpoint of segment AB, then: 2AM=AB and AM=(1/2)…

Angle Bisector Theorem

if ray BX is the bisector of angle ABC, then: ... 2m angle ABX=m…

right angle theorem

straight angle theorem

bisect/trisect theorem

congruent bisect/trisect theorem

If 2 angles are right angles, then they are congruent

If 2 angles are straight angles, then they are congruent

if a (point, segment, ray, or line) bisects/trisects a (segme…

if a (segment, angle) is divided into 2/3 congruent parts the…

right angle theorem

If 2 angles are right angles, then they are congruent

straight angle theorem

If 2 angles are straight angles, then they are congruent

Expansion Postulate

Line Postulate

Plane Postulate

Flat Plane Postulate

A line contains at least two points. A plane contains at leas…

Any two points in space lie in exactly one line

Three distinct noncollinear points lie in exactly one plane

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

Expansion Postulate

A line contains at least two points. A plane contains at leas…

Line Postulate

Any two points in space lie in exactly one line

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points of a line can be put into one-to-one correspondenc…

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

Consider ray OB and a point A on one side of ray OB. Every ra…

If point B is in the interior of Angle AOC, then the measurem…

Ruler Postulate

The points of a line can be put into one-to-one correspondenc…

Segment Addition Postulate

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

(Segment Addition Postulate) If B is b…

(Post. 5) A line contains at least _ p…

(Post. 6) Through any two points...

(Post. 7) Through any three noncolline…

AB + BC = AC

2, 3, 4

there is exactly one line

there is exactly one plane

(Segment Addition Postulate) If B is b…

AB + BC = AC

(Post. 5) A line contains at least _ p…

2, 3, 4

Postulate 1.1

Postulate 1.2

Postulate 1.3

Postulate 1.4

Given any TWO distinct POINTS in space, there is exactly ONE…

Given any THREE distinct POINTS in space NOT ON THE SAME LINE…

The line determined by any two distinct points in a plane is…

No plane contains all points in space.

Postulate 1.1

Given any TWO distinct POINTS in space, there is exactly ONE…

Postulate 1.2

Given any THREE distinct POINTS in space NOT ON THE SAME LINE…

If B is between A and C, then

If point D lies in the interior of ㄥAB…

If ㄥABC is a straight angle and D is a…

A line contains at least _____ points;…

AB + BC = AC

mㄥABD + mㄥCBD = mㄥABC

mㄥABD + mㄥCBD = 180॰

2, 3, 4

If B is between A and C, then

AB + BC = AC

If point D lies in the interior of ㄥAB…

mㄥABD + mㄥCBD = mㄥABC

If two angles are right angles

If two angles are straight angles

If a conditional statement is true

Lines

Then they are congruent

Then they are congruent

Then the contrapositive of the statement is true( if a, then…

They are made up of points with arrows at the end and are str…

If two angles are right angles

Then they are congruent

If two angles are straight angles

Then they are congruent

Ruler Postulate

Segment Addition Postulate

Congruent Figures

Congruent Segments

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

Have the same size and shape

Have equal lengths

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

Postulate

Ruler Postulate

Segment Addition Postulate

Midpoint Formula

Something we believe to be true but cannot prove.

The distance between two points is the absolute value of the…

If a point is between to other points then they MUST be colli…

M = {(x2+x1)/2 , (y2+y1)/2} or reverse {(x1+x2)/2 , (y1+y2)/2}

Postulate

Something we believe to be true but cannot prove.

Ruler Postulate

The distance between two points is the absolute value of the…

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 non-collinear 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…

points, lines and planes

line segment

ray

angle

undefined terms

a line with two endpoints;... set containing all points includin…

a line with one endpoint

union of two rays that share a common endpoint

points, lines and planes

undefined terms

line segment

a line with two endpoints;... set containing all points includin…

(Segment Addition Postulate) If B is b…

(Post. 5) A line contains at least _ p…

(Post. 6) Through any two points...

(Post. 7) Through any three noncolline…

AB + BC = AC

2, 3, 4

there is exactly one line

there is exactly one plane

(Segment Addition Postulate) If B is b…

AB + BC = AC

(Post. 5) A line contains at least _ p…

2, 3, 4

Ruler Postulate

Segment Addition Postulate

Congruent Figures

Congruent Segments

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

Have the same size and shape

Have equal lengths

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

Point-Line-Plane Postulate: a. Unique…

Point-Line-Plane Postulate: b. Number…

Point-Line-Plane Postulate: c. Dimensi…

Point-Line-Plane Postulate: c. Dimensi…

Through any two points there is exactly one line. If the two…

Every line is a set of points that can be put into a one-to-o…

There are at least two points in space.

Given a line in a plane, there is at least one point in the p…

Point-Line-Plane Postulate: a. Unique…

Through any two points there is exactly one line. If the two…

Point-Line-Plane Postulate: b. Number…

Every line is a set of points that can be put into a one-to-o…

Expansion Postulate

Line postulate

Plane postulate

Flat plane postulate

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

Any two points in space lie in exactly one line

Three distinct noncollinear points lie in exactly one plane

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

Expansion Postulate

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

Line postulate

Any two points in space lie in exactly one line

Postulate 5

Postulate 6

Postulate 7

Postulate 8

The Dimension Postulate ... A line contains at least 2 points ... A…

Two points determine exactly one line

Any 3 points determine exactly one line (shows existence) ... 3…

If two points lie in a plane, the line that contains them lie…

Postulate 5

The Dimension Postulate ... A line contains at least 2 points ... A…

Postulate 6

Two points determine exactly one line

Postulate 1... Ruler Postulate

Postulate 2... Segment Addition Postulate

Postulate 3... Protractor Postulate

Postulate 4... Angle Addition Postulate

Ruler Postulate- ... Points on a line can be paired with real nu…

Segment Addition Postulate-... If B is between A and C, the AB +…

Protractor Postulate-... all rays of the interior of a straight…

Angle Addition Postulate-... If B lies on the interior of <AOC,…

Postulate 1... Ruler Postulate

Ruler Postulate- ... Points on a line can be paired with real nu…

Postulate 2... Segment Addition Postulate

Segment Addition Postulate-... If B is between A and C, the AB +…

Theorem 0

Theorem 1

Theorem (=~=) segs reflex

Theorem (=~=) segs sym

If 2 lines intersect, then they intersect at exactly one uniq…

A conditional is true if and only if it's contrapositive is t…

The congruence of segments is reflexive.

The congruence of segments is symmetric.

Theorem 0

If 2 lines intersect, then they intersect at exactly one uniq…

Theorem 1

A conditional is true if and only if it's contrapositive is t…

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 plains 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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

(How to measure with a ruler) Any line AB is equal in length…

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

(How to measure with a protactor) Any angle OAB is equal to t…

If P is in the interior of RST, then mRST=mRSP+mPST

Ruler Postulate

(How to measure with a ruler) Any line AB is equal in length…

Segment Addition Postulate

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

Through any two points there is exactl…

Through any three noncollinear points…

If two points lie in a plane, then the…

If two lines intersect, then they inte…

Through any two points there is exactly ___ ____.

Through any three noncollinear points there is exactly ___ __…

If two points lie in a plane, then the _________ containing t…

If two lines intersect, then they intersect in exactly ______…

Through any two points there is exactl…

Through any two points there is exactly ___ ____.

Through any three noncollinear points…

Through any three noncollinear points there is exactly ___ __…

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate; The points on a line can be paired with the…

Segment Addition Postulate; If B is between A and C, then ... AB…

Protractor Postulate; We can measure angles with protractors.

Angle Addition Postulate; If point B lies in the interior of…

Postulate 1

Ruler Postulate; The points on a line can be paired with the…

Postulate 2

Segment Addition Postulate; If B is between A and C, then ... AB…

Angle Bisector Theorem

Line Postulate

Plane Postulate

Plane Intersection Postulate

If a ray is an angle bisector, then the sum of the two congru…

Through any two points there is exactly one line.

A plane contains at least three non-collinear points. Through…

If two planes intersect, they intersect in a line.

Angle Bisector Theorem

If a ray is an angle bisector, then the sum of the two congru…

Line Postulate

Through any two points there is exactly one line.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

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=m<A…

Ruler Postulate

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

Segment Addition Postulate

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

undefined term

point

line

plane

a term that cannot be defined by another figure (ex: points,…

names a location that has no size, represented by a dot and a…

a straight path that has no thickness, represented by a lower…

flat surface that has no thickness and extends forever, repre…

undefined term

a term that cannot be defined by another figure (ex: points,…

point

names a location that has no size, represented by a dot and a…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

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=m<A…

Ruler Postulate

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

Segment Addition Postulate

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 paired with the real numbers in s…

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=m<A…

Postulate 1: Ruler Postulate

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

Postulate 2: Segment Addition Postulate

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

Postulate 5

Postulate 6

Postulate 7

Postulate 8

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

Through any two points, there is exactly one line.

Through any three points, there is at least one plane and thr…

If two points are in a plane, then the line that contains the…

Postulate 5

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

Postulate 6

Through any two points, there is exactly one line.

Ruler Postulate

Segement Addition Postulate

Protractor Postulate

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 a given plane, chose any point O between A and B. Consider…

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

Ruler Postulate

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

Segement Addition Postulate

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

Definition of a Line

Definition of Intersecting Lines

Definition of Intersecting Planes

Definition of a Plane

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…

Definition of a Line

Through any two points there is exactly one line.

Definition of Intersecting Lines

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

Ruler Postulate

Segment addition postulate

Protractor Postulate

Angle Addition Postulate

On a coordinate system, the absolute value of the difference…

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

If ray OA = 0 and ray OB = 180, then the absolute value of th…

mLboc + mLaob = mLaoc. If the interior of angle AOC is angle…

Ruler Postulate

On a coordinate system, the absolute value of the difference…

Segment addition postulate

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

Postulate 5

Postulate 6

Postulate 7

Postulate 8

A line contains at least two points; a plane contains three p…

Through any two points, there is exactly one line

Through any three points, there is exactly one plane and thro…

If two points are in one plane, then the line that contains t…

Postulate 5

A line contains at least two points; a plane contains three p…

Postulate 6

Through any two points, there is exactly one line

net

isometric drawing

orthographic drawing

point

a 2 dimensional diagram that you can fold to form a a 3 dimen…

shows a corner view of a three dimensional figure ... (front and…

shows three separate views: a top view, a front view, and a r…

indicates a location and had no size

net

a 2 dimensional diagram that you can fold to form a a 3 dimen…

isometric drawing

shows a corner view of a three dimensional figure ... (front and…

Segment Length Addition Postulate (SLAP)

Angle Measure Addition Postulate (AMAP)

A line contains at least...

A plane contains at least...

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

If point B lies in the interior of ∠AOC, then m∠AOB+m∠BOC=180.

...2 points.

...3 points not all in one line.

Segment Length Addition Postulate (SLAP)

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

Angle Measure Addition Postulate (AMAP)

If point B lies in the interior of ∠AOC, then m∠AOB+m∠BOC=180.

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 intersect in exactly on…

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

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 intersect in exactly on…

Ruler Postulate

Segment addition postulate

Protractor Postulate

Angle Addition Postulate

On a coordinate system, the absolute value of the difference…

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

If ray OA = 0 and ray OB = 180, then the absolute value of th…

mLboc + mLaob = mLaoc. If the interior of angle AOC is angle…

Ruler Postulate

On a coordinate system, the absolute value of the difference…

Segment addition postulate

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

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3

Postulate 4

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

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

How to set up and use a protractor

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

Postulate 1: Ruler Postulate

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

Postulate 2: Segment Addition Postulate

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

Postulate 1 ~ 1. (Ruler Postulate)

Postulate 1 ~ 2. (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 4 ~ 1. (Angle Addition Postu…

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

Once a coordinate system has been chosen in this way, the dis…

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

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

Postulate 1 ~ 1. (Ruler Postulate)

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

Postulate 1 ~ 2. (Ruler Postulate)

Once a coordinate system has been chosen in this way, the dis…

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 AB in a given plane, choose any point O between A and B. C…

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 paired with the real numbers i…

Postulate 2: Segment Addition Postulate

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

Point-line-plane Postulate

Line Intersection Theorem

Distance Postulate

Triangle Inequality Postulate

a.Unique line assumption... through any two points there is exac…

two different lines intersect in at most once

a. Uniqueness property On a coordinatized line, there is a un…

The sum of the lengths of any two sides of a triangle is grea…

Point-line-plane Postulate

a.Unique line assumption... through any two points there is exac…

Line Intersection Theorem

two different lines intersect in at most once

true

false

true

false

Through any 2 points there is exactly one line (t or f)

Through any 2 points there isn't always a line (t or f)

Through any 3 noncollinear points there is exactly one plane…

Through any 4 noncollinear points there is exactly one plane…

true

Through any 2 points there is exactly one line (t or f)

false

Through any 2 points there isn't always a line (t or f)

Through any two points there is exactl…

Through any three non collinear points…

If two points lie on a plane, then the…

If two lines intersect, then they inte…

...

...

...

...

Through any two points there is exactl…

...

Through any three non collinear points…

...

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Right Angle Congruence Theorem

Vertical angles are conguent.

If two angles are supplements of the same angle or a congruen…

If two angles are complements of the same angle, then the two…

All right angles are congruent

Vertical Angles Theorem

Vertical angles are conguent.

Congruent Supplements Theorem

If two angles are supplements of the same angle or a congruen…

Inductive reasoning

Conjecture

Deductive reasoning

Point

reasoning based on patterns you observe

a concluding statement reached by using inductive reasoning

process of reasoning logically from given to a conclusion

a location in space

Inductive reasoning

reasoning based on patterns you observe

Conjecture

a concluding statement reached by using inductive reasoning

ruler postulate (postulate one)

segment addition postulate (postulate…

protractor postulate (postulate three)

angle addition postulate (postulate fo…

the distance between two points equals the absolute value of…

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

- on line AB in a given plane, choose any point O between A a…

- if point b lies in the interior of angle AOC, then:... m<AOB +…

ruler postulate (postulate one)

the distance between two points equals the absolute value of…

segment addition postulate (postulate…

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