#### Study sets matching "chapter 1 geometry theorems"

#### Study sets matching "chapter 1 geometry theorems"

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

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

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…

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

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…

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

(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

Post. 1-1-1

Post. 1-1-2

Post. 1-1-3

Post. 1-1-4

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…

Post. 1-1-1

Through any two points there is exactly one line.

Post. 1-1-2

Through any three noncollinear points there is exactly one pl…

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…

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:

Line Segments:

Rays:

They're dots represented by capital letters

Made up of points and are straight. The line will have arrows…

Made up of points and are straight, but has a definite beginn…

Made up of points and are straight. It begins at an endpoint…

Points:

They're dots represented by capital letters

Lines:

Made up of points and are straight. The line will have arrows…

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…

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

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... 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 +…

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

Post. 1-1-1

Post. 1-1-2

Post. 1-1-3

Post. 1-1-4

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…

Post. 1-1-1

Through any two points there is exactly one line.

Post. 1-1-2

Through any three noncollinear points there is exactly one pl…

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…

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

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,…

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

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 ___ __…

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

2.1 - Properties of Segment Congruence

2.2 - Properties of Angle Congruence

2.3 - Right Angles Congruence Theorem

2.4 - Congruent Supplements Theorem

Segment congruence is reflexive, symmetric, and transitive.

Angle congruence is reflexive, symmetric, and transitive.

All right angles are congruent.

If two angles are supplementary to the same angle (or to cong…

2.1 - Properties of Segment Congruence

Segment congruence is reflexive, symmetric, and transitive.

2.2 - Properties of Angle Congruence

Angle congruence is reflexive, symmetric, and transitive.