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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…

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 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

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 1.1

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…

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…

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…

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…

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

diagonals of a rectangle

triangle inequality theorem

midpoint theorem

addition property of equality

if the diagonals of a parallelogram are congruent, then the p…

the sum of the lengths of any two sides of a triangle must be…

if M is the midpoint of AB than AM = BM

a=b then a+c= b+c

diagonals of a rectangle

if the diagonals of a parallelogram are congruent, then the p…

triangle inequality theorem

the sum of the lengths of any two sides of a triangle must be…

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 2 points lie in a plane, then the line containing those po…

if 2 lines intersect they intersect at exactly 1 point

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 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

Postulate 1

Postulate 2

The Pythagorean Theorem(ch.2)

The Triangle Angle Sum Theorem(ch.2)

two points determine a line

three noncollinear points determine a plane

The square of the hypotenuse of a right triangle is equal to…

The sum of the angles of a triangle is 180 degrees

Postulate 1

two points determine a line

Postulate 2

three noncollinear points determine a plane

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…

Through 2 points

Through any 3 points noncollinear

A line contains

If two points lie on a plane

There is only one line

There is only one plane

2 points

The entire line connecting them lies on that plane

Through 2 points

There is only one line

Through any 3 points noncollinear

There is only one plane

Third Angles Theorem

SSS Postulate

SAS postulate

ASA postulate

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

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

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

If two angles and the included side of one triangle are congr…

Third Angles Theorem

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

SSS Postulate

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

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

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

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…

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

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.

(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…

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…

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…

Postulate 22

Theorem 6.2

Theorem 6.4

Theorem 6.5

if 2 angles of one triangle are congruent to 2 angles of anot…

if the corresponding side lengths of 2 triangles are proporti…

if a line parallel to one side of a triangle intersects the o…

if a line divides 2 sides of a triangle proportionally, then…

Postulate 22

if 2 angles of one triangle are congruent to 2 angles of anot…

Theorem 6.2

if the corresponding side lengths of 2 triangles are proporti…

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…

Postulate 1-1-1

Postulate 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 at 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…

1-1-1 Points, Lines, and Planes

1-1-2 Points, Lines, and Planes

1-1-3 Points, Lines, and Planes

1-1-4 Intersection of Lines and Planes

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 plane containing those…

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

1-1-1 Points, Lines, and Planes

Through any two points there is exactly one line.

1-1-2 Points, Lines, and Planes

Through any three noncollinear points there is exactly one pl…

Chords and Arcs Theorem

Converse of Chords and Arcs Theorem

Tangent Theorem

Converse of Tangent Theorem

In a circle or in congruent circles, the arcs of congruent ch…

In a circle or in congruent circles, the chords of congruent…

A line that is tangent to a circle is perpendicular to a radi…

A line that is perpendicular to a radius of a circle at its e…

Chords and Arcs Theorem

In a circle or in congruent circles, the arcs of congruent ch…

Converse of Chords and Arcs Theorem

In a circle or in congruent circles, the chords of congruent…

Chapter 3:

Theorem 3-1

Postulate 10

Theorem 3-2

Chapter 3:

if 2 parallel planes are cut by a 3rd plane, then the lines o…

if 2 parallel lines are cut by a transversal, then correspond…

if 2 parallel lines are cut by a transversal, then alternate…

Chapter 3:

Chapter 3:

Theorem 3-1

if 2 parallel planes are cut by a 3rd plane, then the lines o…

Congruent

Coencentric

Definition of a Circle

Circumscribed

____ circles have similar radii

__________ circles have the same center

Set of points equidistant from a given point

All of polygon's vertices touch a circle in a(n) ________ cir…

Congruent

____ circles have similar radii

Coencentric

__________ circles have the same center

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, 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

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

Segment Addition Postulate

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

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…

Acute triangle

Equiangular triangle

Obtuse triangle

Right triangle

A triangle in which all of the angles are acute. It has three…

A triangle with all angles congruent. It has three congruent…

A triangle with an obtuse angle. An obtuse angle is any angle…

A triangle with a right angle. A right angle is any angle tha…

Acute triangle

A triangle in which all of the angles are acute. It has three…

Equiangular triangle

A triangle with all angles congruent. It has three congruent…

The Ruler Postulate

The Protractor Postulate

Segment Addition Postulate/The Between…

Angle Addition Postulate/The Betweenne…

points on a line can be numbered so that positive number diff…

you can measure angles

If A-B-C, then AB + BC = AC

∠AOB + ∠BOC = ∠AOC

The Ruler Postulate

points on a line can be numbered so that positive number diff…

The Protractor Postulate

you can measure angles

Two points are symmetric with respect…

In a plane, two points each equidistan…

Equal corresponding angles

Equal alternate interior angles

iff the line is the perpendicular bisector of the line segmen…

determine the perpendicular bisector of the line segment.

mean that lines are parallel.

mean that lines are parallel.

Two points are symmetric with respect…

iff the line is the perpendicular bisector of the line segmen…

In a plane, two points each equidistan…

determine the perpendicular bisector of the line segment.

AAS Theorem: 4-5-2

The Isosceles Triangle Theorem: 4-8-1

Corollary of an equiangular triangle:…

Corollary of triangle: 4-2-3

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

If two sides of a triangle are congruent, then the angles opp…

An equilateral triangle is also equiangular.

An equilateral triangle has three 60 Degree angles

AAS Theorem: 4-5-2

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

The Isosceles Triangle Theorem: 4-8-1

If two sides of a triangle are congruent, then the angles opp…

(ch 1) through any two points there is…

(ch 1) through any three noncollinear…

(ch 1) if two points lie in a plane, t…

(ch 1) if two lines intersect, then th…

...

...

...

...

(ch 1) through any two points there is…

...

(ch 1) through any three noncollinear…

...

MULTIPLICATION THEOREM OF CONGRUENCE

DIVISION THEOREM OF CONGRUENCE

If two angles are right angles, then t…

If two angles are complementary to the…

If congruent segments/angles are multiplied by a constant, th…

If congruent segments/angles are divided by a non-zero consta…

...

...

MULTIPLICATION THEOREM OF CONGRUENCE

If congruent segments/angles are multiplied by a constant, th…

DIVISION THEOREM OF CONGRUENCE

If congruent segments/angles are divided by a non-zero consta…

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

if point B lies in the interior of <AO…

two

three

segment additions postulate

angle addition postulate

a line contains atleast __ points

a plane contains at lease ___ points not all in one line

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

segment additions postulate

if point B lies in the interior of <AO…

angle addition postulate

Ruler Postulate

Segmant Addition Postulate

Protractor Postulate

Angle Addition Postulate

the points on a line can be matched one to one with the real…

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

one ray of an angle can be paired with 0 degrees and its oppo…

if you have two angles that share a common ray, you can add t…

Ruler Postulate

the points on a line can be matched one to one with the real…

Segmant Addition Postulate

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

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem/Side…

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

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two angles are in proportion, then the triang…

If a line parallel to one side of a triangle intersects the o…

AA Similarity Postulate

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

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…

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)