# 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 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 t…

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

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 (segmen…

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

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

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)A…

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 ar…

Midpoint Theorem

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

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

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

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

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

No plane contains all points in space.

Postulate 1.1

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

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 in…

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 in…

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 correspondence…

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

(Segment Addition Postulate) If B is be…

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

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

(Post. 7) Through any three noncollinea…

AB + BC = AC

2, 3, 4

there is exactly one line

there is exactly one plane

(Segment Addition Postulate) If B is be…

AB + BC = AC

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

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 pla…

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

If two lines intersect, then they intersect in exactly one poi…

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 pla…

If B is between A and C, then

If point D lies in the interior of ㄥABC…

If ㄥABC is a straight angle and D is an…

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 ㄥABC…

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 b…

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

If two angles are right angles

Then they are congruent

If two angles are straight angles

Then they are congruent

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 beginni…

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

Points:

They're dots represented by capital letters

Lines:

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

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 exactl…

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

Through any three non-collinear 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 exactl…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Postulate 1

Ruler Postulate

Postulate 2

Segment Addition Postulate

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 pla…

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

If two lines intersect, then they intersect in exactly one poi…

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 pla…

Point-Line-Plane Postulate: a. Unique L…

Point-Line-Plane Postulate: b. Number L…

Point-Line-Plane Postulate: c. Dimensio…

Point-Line-Plane Postulate: c. Dimensio…

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

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

There are at least two points in space.

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

Point-Line-Plane Postulate: a. Unique L…

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

Point-Line-Plane Postulate: b. Number L…

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

points, lines and planes

line segment

ray

angle

undefined terms

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

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 including…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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 t…

Segment Addition Postulate

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

(Segment Addition Postulate) If B is be…

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

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

(Post. 7) Through any three noncollinea…

AB + BC = AC

2, 3, 4

there is exactly one line

there is exactly one plane

(Segment Addition Postulate) If B is be…

AB + BC = AC

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

2, 3, 4

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 n…

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

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 num…

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

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

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

Postulate 1... Ruler Postulate

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

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 in…

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 in…

Segment Addition Postulate

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

Theorem 0

Theorem 1

Theorem (=~=) segs reflex

Theorem (=~=) segs sym

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

A conditional is true if and only if it's contrapositive is tr…

The congruence of segments is reflexive.

The congruence of segments is symmetric.

Theorem 0

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

Theorem 1

A conditional is true if and only if it's contrapositive is tr…

Ruler Postulate

Segment Addition Postulate

Congruent Figures

Congruent Segments

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

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 in…

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 d…

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

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 d…

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 t…

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