#### Study sets matching "geometry properties corollaries"

#### Study sets matching "geometry properties corollaries"

Point

Line

Line Segment

Plane

Does not have any size or shape; Used to identify a location

Extends forever in two directtions; There is no infinite numb…

A line connected by two endpoints

Extends forever with no thickness; Must have at least 3 points

Point

Does not have any size or shape; Used to identify a location

Line

Extends forever in two directtions; There is no infinite numb…

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 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 paired with the real numbers i…

Postulate 2 (Segment Addition Postulate)

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

segment addition postulate (2)

angle addition postulate (4)

postulate 5

postulate 6

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

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

through any two points there exists exactly one line

a line contains at least two points

segment addition postulate (2)

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

angle addition postulate (4)

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

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points there is exactly one line

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

A line contains at least two points

A plane contains at least three non collinear points

Postulate 2.1

Through any two points there is exactly one line

Postulate 2.2

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

Unique Line Postulate

Intersecting Lines Postulate

Intersecting Planes Postulate

Plane Postulate

Through any two points there is exactly one line

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

If two planes intersect, then they intersect in exactly one l…

Through any three nonlinear points there is exactly one plane

Unique Line Postulate

Through any two points there is exactly one line

Intersecting Lines Postulate

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

if 2 angles of one triangle are congru…

____ the third angles are congeuent

what are the measures of the angles of…

how many obtuse or right angles can be…

the third angles are congruent

if 2 angles of one triangle are congruent to two angles of an…

each angle of an equiangular triangle has measure 60

in a triangle, there can be at most one right angle or obtuse…

if 2 angles of one triangle are congru…

the third angles are congruent

____ the third angles are congeuent

if 2 angles of one triangle are congruent to two angles of an…

Corollary 1

Corollary 2

Corollary 3

Corollary 4

If two angles of a triangle are congruent to two angles of an…

Each angle of an equiangular triangle had a measure of 60.

In a triangle, there can be at most one right angle or obtuse…

The acute angles of a right triangle are complementary

Corollary 1

If two angles of a triangle are congruent to two angles of an…

Corollary 2

Each angle of an equiangular triangle had a measure of 60.

4.1

4.2

4.3

4.4

the acute angles of a right triangle are complementary

there can be at most one right or obtuse angle in a triangle

a triangle is equilateral if and only if it is equiangular

each angle of an equilateral triangle measures 60 degrees

4.1

the acute angles of a right triangle are complementary

4.2

there can be at most one right or obtuse angle in a triangle

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Opposite rays can be paired with 0 and 180 degrees. Rays bran…

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

Ruler Postulate

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

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 nonlinear points there is exactly one plane…

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

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

Postulate 1-1-1

Through any two points there is exactly one line

Postulate 1-1-2

Through any three nonlinear points there is exactly one plane…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line

Through any three noncollinear points, there is exactly one p…

A line contains at least two points

A plane contains at least three noncollinear points

Postulate 2.1

Through any two points, there is exactly one line

Postulate 2.2

Through any three noncollinear points, there is exactly one p…

Postulate 1-5: Ruler Postulate

Postulate 1-6: Segment Addition Postul…

Postulate 1-7: Protractor Postulate

Postulate 1-8: Angle Addition Postulate

Every point on a line can be paired with a real number. This…

If three pints 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 ra…

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

Postulate 1-5: Ruler Postulate

Every point on a line can be paired with a real number. This…

Postulate 1-6: Segment Addition Postul…

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

Postulate 1.1

Postulate 1.2

Postulate 1.3

Postulate 1.4

Through any 2 points there is exactly one line.

If two lines intersect then they intersect at exactly one poi…

If two planes intersect then they intersect at exactly one li…

Through any 3 Non-Collinear points there is exactly one plane.

Postulate 1.1

Through any 2 points there is exactly one line.

Postulate 1.2

If two lines intersect then they intersect at exactly one poi…

1

2

3

4

If two angles of one triangle are congruent to two angles of…

Each angle of an equiangular triangle has measure of 60.

In a triangle, there can be at most one right angle or obtuse…

The acute angles of a right triangle are complementary.

1

If two angles of one triangle are congruent to two angles of…

2

Each angle of an equiangular triangle has measure of 60.

Theorem 5.3 (Circumcenter Theorem)

Theorem 5.4 (Angle Bisector Theorem)

Theorem 5.5 (Converse of the Angle Bis…

Theorem 5.6 (Incenter Theorem)

The perpendicular bisectors of a triangle intersect at a poin…

If a point is on the bisectors of an angle, then it is equidi…

If a point in the interior of an angle is equidistant from th…

The angle bisectors of a triangle intersect at a point called…

Theorem 5.3 (Circumcenter Theorem)

The perpendicular bisectors of a triangle intersect at a poin…

Theorem 5.4 (Angle Bisector Theorem)

If a point is on the bisectors of an angle, then it is equidi…

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 noncollinear points there is exactly one pl…

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

if two lines intersect, then they intersect in exactly one po…

Postulate 1-1-1

through any two points there is exactly one line

Postulate 1-1-2

through any three noncollinear points there is exactly one pl…

Linear Pair Postulate

Corresponding Angles Postulate

Two Perps Theorem

Perpendicular Transversal Theorem

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

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

If two lines are perpendicular to the same line, then the lin…

If a line is perpendicular to one of two parallel lines, then…

Linear Pair Postulate

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

Corresponding Angles Postulate

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

Segment Addition Postulate

Angle Addition Postulate

Point, Line, Plane Postulate 1

Point, Line, Plane Postulate 2

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

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

Through any two points there exists exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

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

Segment Addition Postulate

Angle Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

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

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR

In a right triangle, the sum of the squares if the lengths of…

If two angles form a linear pair then they are supplementary

Segment Addition Postulate

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

Angle Addition Postulate

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR

if two angles of a triangle are congru…

each angle of an equiangular

in a triangle there is at most

acute angles of a right triangle

another triangle the third angles are congruent

triangle has a measure of 60 degrees

one right angle or one obtuse angle

are complementary

if two angles of a triangle are congru…

another triangle the third angles are congruent

each angle of an equiangular

triangle has a measure of 60 degrees

Right Angles Congruence Theorem

Midpoint Theorem

Ruler Postulate

Segment Addition Postulate

All right angles are congruent

If M is the midpoint of line segment AB, then line segment AM…

Given any 2 points A and B on a line, if A corresponds to 0,…

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

Right Angles Congruence Theorem

All right angles are congruent

Midpoint Theorem

If M is the midpoint of line segment AB, then line segment AM…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three points not on the same line, there is exact…

...

...

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three points not on the same line, there is exact…

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

If three sides of one triangle are congruent to the second tr…

If two sides and the included angle of one triangle are congr…

If two sides and the included side of one triangle are congru…

If two angles and a non included side of one triangle are con…

Side-Side-Side (SSS)

If three sides of one triangle are congruent to the second tr…

Side-Angle-Side (SAS)

If two sides and the included angle of one triangle are congr…

Theorem 4.1

Theorem 4.2

Theorem 4.3

Corollary 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Third Angle Theorem- If two angles of one triangle are congru…

Exterior Angle Theorem- The measure of an exterior angle of a…

The acute angles of a right triangle are complementary.

Theorem 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Theorem 4.2

Third Angle Theorem- If two angles of one triangle are congru…

2.1

2.2

2.3

2.4

Postulate, ... Chapter 2 ... Through any two points there is exactl…

Postulate, ... Chapter 2 ... Through any three non-collinear points…

Postulate, ... Chapter 2 ... A line contains at least two points

Postulate, ... Chapter 2 ... A plane contains at least three non-co…

2.1

Postulate, ... Chapter 2 ... Through any two points there is exactl…

2.2

Postulate, ... Chapter 2 ... Through any three non-collinear points…

Theorem #1 Intersecting Lines

Theorem #2 Intersecting Planes

Segment Addition Postulate

Angle Addition Postulate

If two lines intersect ,then they intersect exactly one point

If two planes intersect ,then they intersect exactly one line

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

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR (…

Theorem #1 Intersecting Lines

If two lines intersect ,then they intersect exactly one point

Theorem #2 Intersecting Planes

If two planes intersect ,then they intersect exactly one line

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, than AB+BC= AC

ruler postulate w angles

if point B lies in the interior of ∠AOC than m∠AOB + m∠BOC =…

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, than AB+BC= AC

Reflexive Postulate

Substitution Postulate

Additive POE Postulate

Subtractive POE Postulate

A quantity is equal to itself

if a=b then a can be substituted for b in any expression

if a=b then a+c = b+c

If a=b then a-c =b-c

Reflexive Postulate

A quantity is equal to itself

Substitution Postulate

if a=b then a can be substituted for b in any expression

If two angles of one triangle are cong…

Each angle of an equiangular triangle…

In a triangle there can be at most

Supplementary Angle Theorem

then the third angles are congruent too

sixty degrees

one right angle or one obtuse angle

All angles which are supplementy to the same or equal angles…

If two angles of one triangle are cong…

then the third angles are congruent too

Each angle of an equiangular triangle…

sixty degrees

Postulate 1: The Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3: The Protractor Postulate

Postulate 4: Angle Addition Postulate

You are able to make a line and coordinatize it.

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

You are able to have a protractor and coordinatize it

if point B lives in the interior of angle AOC, then Mangle

Postulate 1: The Ruler Postulate

You are able to make a line and coordinatize it.

Postulate 2: 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 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 in exactly one po…

Post 1-1-1

Through any two points there is exactly one line

Post 1-1-2

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

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 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…

Postulate 1.1-1

Through any two points there is exactly one line

Postulate 1.1-2

Through any three noncollinear points there is exactly one pl…

Perpendicular Transversal Theorem

Lines Perpendicular to a Transversal T…

6 Vertical Angles Congruence Theorem

Parallel Postulate

If a transversal is perpendicular to one of two parallel line…

In a plane, if two lines are perpendicular to the same line,…

Vertical Angles are congruent.

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

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel line…

Lines Perpendicular to a Transversal T…

In a plane, if two lines are perpendicular to the same line,…

Postulate 1

Postulate 2:

Postulate 3:

Postulate 4:

Ruler Postulate: The points on a line can be paired in a one…

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

Protractor Postulate:... Given a point, X, on line PR, consider…

Angle Addition Postulate:... If point D is in the interior of <A…

Postulate 1

Ruler Postulate: The points on a line can be paired in a one…

Postulate 2:

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

IF TWO LINES ARE PERPENDICULAR,

IF TWO LINES INTERSECT,

IN A PLANE,

IF TWO LINES MEET TO FORM A RIGHT ANGLE

...then they meet to form right angles

...then the vertical angles formed are congruent

... there is exactly one line perpendicular to a given line a…

...then these lines are perpendicular

IF TWO LINES ARE PERPENDICULAR,

...then they meet to form right angles

IF TWO LINES INTERSECT,

...then the vertical angles formed are congruent

2.1: Points, Lines, and Planes Postulate

2.2: Points, Lines, and Planes Postulate

2.3: Points, Lines, and Planes Postulate

2.4: Points, Lines, and Planes Postulate

Through any two points, there is exactly one line

Through any three non-collinear points, there is exactly one…

A line contains at least two points

A plane contains at three non-collinear points

2.1: Points, Lines, and Planes Postulate

Through any two points, there is exactly one line

2.2: Points, Lines, and Planes Postulate

Through any three non-collinear points, there is exactly one…

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

Postulate 1

Postulate 2:

Postulate 3:

Postulate 4:

Ruler Postulate: The points on a line can be paired in a one…

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

Protractor Postulate:... Given a point, X, on line PR, consider…

Angle Addition Postulate:... If point D is in the interior of <A…

Postulate 1

Ruler Postulate: The points on a line can be paired in a one…

Postulate 2:

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

Corollaries

Corollaries

Corollaries

Supplementary Angle Theorem

If two angles of one triangle are congruent to two angles of…

Each angle of an equiangular triangle measures sixty degrees

In a triangle there can be at most one right angle or one obt…

All angles which are supplementy to the same or equal angles…

Corollaries

If two angles of one triangle are congruent to two angles of…

Corollaries

Each angle of an equiangular triangle measures sixty degrees

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 0…

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

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

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

Postulate 1 (Ruler Postulate)

1. The points on a line can be paired with the real numbers 0…

Postulate 2 (Segment Addition Postulate)

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

Right Angles Congruence Theorem

Midpoint Theorem

Ruler Postulate

Segment Addition Postulate

All right angles are congruent

If M is the midpoint of line segment AB, then line segment AM…

Given any 2 points A and B on a line, if A corresponds to 0,…

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

Right Angles Congruence Theorem

All right angles are congruent

Midpoint Theorem

If M is the midpoint of line segment AB, then line segment AM…

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

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

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

Use a protractor to measure angles

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

Ruler postulate

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

Segment addition postulate

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

(Postulate 1-5) Ruler Postulate

(Postulate 1-7) Protractor Postulate

(Postulate 1-8) Angle Addition Postulate

(Postulate 1-9) Linear Pair Postulate

Every point on a line can be paired with a real number. This…

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

If point B is in the interior of angle <AOC, then m<AOB + m<B…

If 2 angles form a linear pair, then they are supplementary

(Postulate 1-5) Ruler Postulate

Every point on a line can be paired with a real number. This…

(Postulate 1-7) Protractor Postulate

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

Corollary 1

Corollary 2

Corollary

Corollary 1: Rt. Triangles

The perpendicular segment from a point to a line is the short…

The perpendicular segment from a point to a plane is the shor…

If three parallel lines intersect 2 transversals, then they d…

When the altitude is drawn to the hypotenuse of a right trian…

Corollary 1

The perpendicular segment from a point to a line is the short…

Corollary 2

The perpendicular segment from a point to a plane is the shor…

Postulate 10

Postulate 11

Postulate 12

Postulate 13

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

If two lines are cut by a transversal and corresponding angle…

If the three sides of a triangle are congruent to the corresp…

If two sides and the included angle of a triangle are congrue…

Postulate 10

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

Postulate 11

If two lines are cut by a transversal and corresponding angle…

Through any two points there is

Through any three noncollinear points…

If two points lie on a plane, then the…

Ruler Postulate

exactly one line

one plane containing them

lies in the plane

The points on a line can be put into a one-to-one corresponde…

Through any two points there is

exactly one line

Through any three noncollinear points…

one plane containing them

A: Congruent Triangles

A: Distance from a point to a line

A:Reflection of a line

A:Parallelogram

Triangles are congruent if there is a one-to-one corresponden…

The distance from a point P to a line l is the length of the…

A reflection in a line l assigns to each point P in the plane…

a quadrilateral in which each pair of opposite sides is paral…

A: Congruent Triangles

Triangles are congruent if there is a one-to-one corresponden…

A: Distance from a point to a line

The distance from a point P to a line l is the length of the…

1-1-1 Postulate

1-1-2 Postulate

1-1-3 Postulate

1-1-4 Postulate

Through any two points there is exactly one line.

Through any three nonlinear points there is exactly one plane.

If two points lie in a plane then that line also lies on the…

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

1-1-1 Postulate

Through any two points there is exactly one line.

1-1-2 Postulate

Through any three nonlinear points there is exactly one plane.

Determining a-Line Postulate

Betweenness of points theorem

Betweenness of Rays Theorem

Half Corollary (to the definition of b…

2 points determine a line

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

If Ray OB is between rays OA and OC, then <AOB +BOC = <AOC

If something is being bisected, the a portion of it is equal…

Determining a-Line Postulate

2 points determine a line

Betweenness of points theorem

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