# Study sets matching "chapter 1 geometry theorems"

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Ruler Postulate- Postulate 1

Segment Addition Postulate- Postulate 2

Protractor Postulate- Postulate 3

Angle Addition Postulate- Postulate 4

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

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 =…

Ruler Postulate- Postulate 1

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

Segment Addition Postulate- Postulate 2

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

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

midpoint formula

distance formula

the distance between points A and B, written as AB, is the abs…

if B is between A and C, the AB + BC = AC. If AB + BC = AC, th…

the coordinates of the midpoint of a segment are the averages…

if A(x1-y1) and B(x2-y2) are points in a coordinate plane, the…

ruler postulate

the distance between points A and B, written as AB, is the abs…

segment addition postulate

if B is between A and C, the AB + BC = AC. If AB + BC = AC, th…

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…

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

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 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

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 1

Postulate 2

Triangle Sum Theorem

Two Circle Theorem

Two points determine a line

Three non collinear points determine a plane

The sum of triangle angles = 180°

C= πd and A=πr²

Postulate 1

Two points determine a line

Postulate 2

Three non collinear points determine a plane

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…

Linear Pair Postulate

Protractor Postulate

Angle Addition Postulate

Segment Addition Postulate

If the exterior sides of two adjacent angles form a straight l…

Ray OA is paired with 0, and Ray OB with 180. Measure of angle…

If point S lies in the interior of angle QRT then the measure…

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

Linear Pair Postulate

If the exterior sides of two adjacent angles form a straight l…

Protractor Postulate

Ray OA is paired with 0, and Ray OB with 180. Measure of angle…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

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

Through any two points there is exactly one line

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

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

Postulate 1

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

Postulate 2

Through any two points there is exactly one line

segment addition postulate

angle addition postulate

postulate 5

postulate 6

states that if B is on line AC then AB+BC=AC

states that if a figure contains three angles, the two smalles…

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

through any two points there is exactly one line

segment addition postulate

states that if B is on line AC then AB+BC=AC

angle addition postulate

states that if a figure contains three angles, the two smalles…

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 noncollinear points lie in exactly one plane.

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

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

points on a line can be paired with real numbers, the distance…

if B is between A and C then AB plus BC equals AC

of rays of the interior of a straight angle and the sides of a…

if B lies on interior of <AOC then m<AOB plus m<BOC equals m<A…

ruler postulate

points on a line can be paired with real numbers, the distance…

segment addition postulate

if B is between A and C then AB plus BC equals AC

point

undefined terms

line

plane

has no size; often represented as a dot; undefined term

only explained by using examples and descriptions; used to def…

geometric figure which extends in two direction without ending…

suggested by a flat wall or table top; extends without ending…

point

has no size; often represented as a dot; undefined term

undefined terms

only explained by using examples and descriptions; used to def…

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…

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…

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

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…

Point

Line

Planes

Collinear

describe a location, no size (labeled with Capital Letters)

go on in both directions forever, infinite points on a line, n…

infinite number of points contained, flat 2D, 3 points minimum…

All the points lie on same line

Point

describe a location, no size (labeled with Capital Letters)

Line

go on in both directions forever, infinite points on a line, n…