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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

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…

Segment Addition Postulate

Angle Addition Postulate

Points of Figures Postulate

Points and Lines Postulate

AB + BC= AC

m∠ABZ+m∠ZBC=m∠ABC

A line contains at least wo points, a plane contains atleast…

Through any two points there is one line

Segment Addition Postulate

AB + BC= AC

Angle Addition Postulate

m∠ABZ+m∠ZBC=m∠ABC

A point on the perpendicular bisector…

A point equidistant from the endpoints…

A point on the bisector of an angle is

A point on or in the interior of an an…

equidistant from the endpoints of the segments

perpendicular bisector of the segement

equidistant from the sides of the angle

sides of an angle lies on the bisector of the angle

A point on the perpendicular bisector…

equidistant from the endpoints of the segments

A point equidistant from the endpoints…

perpendicular bisector of the segement

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 three sides of one triangle are congruent to three sides o…

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

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:

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…

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,…

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

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 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…

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

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…

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 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 Angle Side Theorem

Base Angles Theorem

CITT (Converse to ITT)

ITT (Isosceles Triangle Theorem)

If 2 pairs of corresponding sides and the included angles in…

If two sides of a triangle are congruent the the angles oppos…

If 2 angles of a triangle are congruent then the sides opposi…

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

Side Angle Side Theorem

If 2 pairs of corresponding sides and the included angles in…

Base Angles Theorem

If two sides of a triangle are congruent the the angles oppos…

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

Theorem

Corollary

Segment Addition Postulate

A statement that is accepted as true without proof

Any statement that can be proven

A theorem whose proof comes directly from another theorem.

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

Postulate

A statement that is accepted as true without proof

Theorem

Any statement that can be proven

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 2 Segment Addition Postulate

Postulate 3

Postulate 4 Protractor Postulate

Postulate 5 Angle Addition Postulate

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

Any segment has exactly one midpoint

In a given plane, select any line AB and any point C between…

If D is in the interior of angle ABC, then m angle ABC = m an…

Postulate 2 Segment Addition Postulate

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

Postulate 3

Any segment has exactly one midpoint

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…

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…

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

Postulate 2 Segment Addition Postulate

Postulate 5 Angle Addition Postulate

Theorem 2.4 - Corollary

Postulate 8

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

If D is in the interior of angle ABC, then m angle ABC = m an…

If two lines are perpendicular, then four right angles are fo…

A line contains at least two points. A plane contains at leas…

Postulate 2 Segment Addition Postulate

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

Postulate 5 Angle Addition Postulate

If D is in the interior of angle ABC, then m angle ABC = m an…

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

(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…

...

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

Point

Line

Plane

Collinear Points

has no size; represented by a dot; named by a capital letter

series of points that extend in 2 opposite directions; named…

flat never ending surface; no thickness; named using multiple…

points that are on the same line

Point

has no size; represented by a dot; named by a capital letter

Line

series of points that extend in 2 opposite directions; named…

Properties of kites

Isoceles trapezoids theorem

Conditional statement

Hypothesis

Perpendicular diagonals, one pair of congruent opposite angles

Each pair of base angles are congruent, if and only if diagon…

If p, then q

If p part of conditional statement

Properties of kites

Perpendicular diagonals, one pair of congruent opposite angles

Isoceles trapezoids theorem

Each pair of base angles are congruent, if and only if diagon…

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…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Through any two points there is exactly one line

If two distinct lines intersect, they intersect at one point

If two distinct planes intersect, they intersect at a line

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

Postulate 1

Through any two points there is exactly one line

Postulate 2

If two distinct lines intersect, they intersect at one point

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)