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Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider OB and a point A on one side of OB. The rays of the…

If P is the interior of angleRST, then the measure of angleRS…

Ruler Postulate

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

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 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…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

(1) A line contains at least two points (2) A plane contains…

Through any two points there is exactly one line.

(1) Through any three points there is at least one plane (2)…

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

Postulate 5

(1) A line contains at least two points (2) A plane contains…

Postulate 6

Through any two points there is exactly one line.

theorem 1

theorem 2

theorem 3

theorem 4

If two angles are right angles, then they are congruent

if two angles are straight angles, then they are congruent

If a conditional statement is true, the the contrapositive of…

If angles are supplementary to the same angle, then they are…

theorem 1

If two angles are right angles, then they are congruent

theorem 2

if two angles are straight angles, then they are congruent

Midpoint definition

Segment bisector definition

Congruent segments definition

Angle addition postulate

A point that divides the segment into two congruent segments

a point, line, ray, or other segment that intersects a segmen…

Segments that have the same length

Two little angles make one big angle

Midpoint definition

A point that divides the segment into two congruent segments

Segment bisector definition

a point, line, ray, or other segment that intersects a segmen…

Through any two points

If two lines intersect then

If two distinct planes intersect then

Through any 3 non-collinear points

There is exactly one line.

They intersect at exactly one point.

They intersect at exactly one line.

There is one plane.

Through any two points

There is exactly one line.

If two lines intersect then

They intersect at exactly one point.

Postulate

Ruler Postulate

Congruent Segments

Segment Addition Postulate

A subject we accept as being true without truly proving it

You can find the distance between any two point on a line.

Two segments that have the same length

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

Postulate

A subject we accept as being true without truly proving it

Ruler Postulate

You can find the distance between any two point on a line.

Linear Pair Postulate

vertical angles theorem

Protractor Postulate

Angle Addition Postulate

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

vertical angles are congruent

every angles has a degree measure that can be measured with a…

if B is the interior of /_ AOC then m/_AOB + m/_BOC = /_AOC

Linear Pair Postulate

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

vertical angles theorem

vertical angles are congruent

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 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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Every line segment has a length that can be measured with a r…

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

Every angle has a degree measure that can be measured with a…

If B is in the interior of <RST, then m<RST=m<RSP+m<PST

Ruler Postulate

Every line segment has a length that can be measured with a r…

Segment Addition Postulate

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

If two angles are supplementary to the…

If two angles form a linear pair, then…

If two angles are complementary to the…

All right angles are congurent

Congruent Supplements Theorem

Linear Pair Theorem

Congruent Complements Theorem

Right Angle Congruence Theorem

If two angles are supplementary to the…

Congruent Supplements Theorem

If two angles form a linear pair, then…

Linear Pair Theorem

Complementary Angles

Congruent Angles

Congruent Complements Theorem

Congruent Segments

Two angles whose measures have the sum of 90 degrees.

Angles that have the same measure.

If two angles are complementary to the same angle or to congr…

Segments that have the same length.

Complementary Angles

Two angles whose measures have the sum of 90 degrees.

Congruent Angles

Angles that have the same measure.

Segment addiction postulate

Angle addition postulate

Supplement theorem

Complement theorem

If A, B, and C are collinear, then point B is between A and C…

D is in the interior of <ABC if and only if m<ABD + m<DBC = m…

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

If the non common sides of two adjacent angles form a right a…

Segment addiction postulate

If A, B, and C are collinear, then point B is between A and C…

Angle addition postulate

D is in the interior of <ABC if and only if m<ABD + m<DBC = m…

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 exact…

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

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

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

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

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same Side Interior Angles Theorem

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

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

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

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

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

SSS Postulate (Side-side-side)

SAS Postulate (side-angle-side)

ASA Postulate (angle-side-angle

AAS Postulate (angle-angle-side)

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

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

SSS Postulate (Side-side-side)

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

SAS Postulate (side-angle-side)

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

Angle Addition Postulate

Segment Addition Postulate

Ruler Postulate

Protractor Postulates

2 adjacent angles = a whole; angle abc + cbd = abd

Segment 1 + Segment 2 = the Whole; ab+bc=ac

Points on a number line can be matched up with real numbers

Rays can be matched with real numbers

Angle Addition Postulate

2 adjacent angles = a whole; angle abc + cbd = abd

Segment Addition Postulate

Segment 1 + Segment 2 = the Whole; ab+bc=ac

Through any two points there is exactl…

If two line intersect, then they inter…

If two planes intersect, their interse…

Through any 3 noncollinear points ther…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactl…

Postulate 1-1

If two line intersect, then they inter…

Postulate 1-2

Same-Side Interior Angles POSTULATE

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Corresponding Angles Theorem

If a transversal intersects two parallel lines then the same-…

If a transversal intersects two parallel lines then alternate…

If a transversal intersects two parallel lines then alternate…

If a transversal intersects two parallel lines then correspon…

Same-Side Interior Angles POSTULATE

If a transversal intersects two parallel lines then the same-…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines then alternate…

Addition Property Of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b, then a+c=b+c... If a=b and j=k, then a+j=b+k

If a=b, then a-c=b-c... If a=b and j=k, then a-j=b-k

If a=b, then wa=wb... if c=d and r=s, then cr=ds

If p=q, then p/q=q/p

Addition Property Of Equality

If a=b, then a+c=b+c... If a=b and j=k, then a+j=b+k

Subtraction Property of Equality

If a=b, then a-c=b-c... If a=b and j=k, then a-j=b-k

Midpoint

Supplementary Angles

Perpendicular Lines

Congruent Angles

The point that divides, or bisects, a segment into two congru…

Two angles whose measures have the sum of 180 degrees

Two lines that intersect to form a right angle

Angles that have the same measure

Midpoint

The point that divides, or bisects, a segment into two congru…

Supplementary Angles

Two angles whose measures have the sum of 180 degrees

Postulate 2

Postulate 4

Postulate 5

Postulate 6

Segment addition postulate

The whole of an angle is the sum of its parts - Angle additio…

A line contains at least 2 points; a plane contains at least…

through any two points there is exactly one line

Postulate 2

Segment addition postulate

Postulate 4

The whole of an angle is the sum of its parts - Angle additio…

Distance Postulate

Ruler Postulate

Ruler Placement Postulate

Line Postulate

To every pair of different points there corresponds a unique…

The points of a line can be placed in correspondence with the…

Given two points P and Q of a line, the coordinate system can…

For every two different points there is exactly one line that…

Distance Postulate

To every pair of different points there corresponds a unique…

Ruler Postulate

The points of a line can be placed in correspondence with the…

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…

midpoint

colinear

straight angle

acute angle

it is a midpoint if and only if it divides a segment into two…

3 or more points on the same line; CONDITIONAL: if it is coli…

the sides of a straight angle form a line; CONDITIONAL: if it…

is less than a right angle; CONDITIONAL: if it is an acute an…

midpoint

it is a midpoint if and only if it divides a segment into two…

colinear

3 or more points on the same line; CONDITIONAL: if it is coli…

Postulate 2

Postulate 4

Postulate 5

Postulate 6

Segment addition postulate

The whole of an angle is the sum of its parts - Angle additio…

A line contains at least 2 points; a plane contains at least…

through any two points there is exactly one line

Postulate 2

Segment addition postulate

Postulate 4

The whole of an angle is the sum of its parts - Angle additio…

Parallel lines

Perpendicular

Skew lines

Parallel planes

Coplanar lines that do not intersect.

Lines that intersect to form a right angle.

Non-coplanar lines that do not intersect.

Planes that do not intersect.

Parallel lines

Coplanar lines that do not intersect.

Perpendicular

Lines that intersect to form a right angle.

Midpoint theorem

Addition property of =

Subtraction property of =

Multiplication property of =

If M is the midpoint of segment AB, then segment AM ≅ MB.

If a=b, then a+c = a+b.

If a=b, then a-c = b-c.

If a=b, then a x c = b x c.

Midpoint theorem

If M is the midpoint of segment AB, then segment AM ≅ MB.

Addition property of =

If a=b, then a+c = a+b.

If two angles are right angles, then t…

If two angles are straight angles, the…

If angles or segments are congruent to…

If angles or segments are congruent to…

Theorem

Theorem

Theorem

Theorem

If two angles are right angles, then t…

Theorem

If two angles are straight angles, the…

Theorem

Postulate 2/Segment Addition Postulate

congruent

congruent segments

midpoint of a segment

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

the term used to describe two objects with the same size and…

segments that have equal lengths

the point that divides a segment into two congruent segments

Postulate 2/Segment Addition Postulate

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

congruent

the term used to describe two objects with the same size and…

(D1) If an angle is a 90 degree angle,…

(D2) If an angle is a 180 degree angle…

(D3) If two angles or segments have th…

(D4) If a point/ray/line _______ a seg…

Right Angle

Straight Angle

Congruent

Bisects

(D1) If an angle is a 90 degree angle,…

Right Angle

(D2) If an angle is a 180 degree angle…

Straight Angle

Segment Addition Postulate

Angle Addition Postulate

Corresponding Angles Postulate

SSS Congruence Postulate

If B is between A and C, then AB + BC = AC (the two parts mus…

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

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

If the 3 sides of one triangle are congruent to the three sid…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC (the two parts mus…

Angle Addition Postulate

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

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Same-side Interior Angle Postulate... If…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a tran…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

Postulate 5

Postulate 6

Postulate 7

Postulate 8

A line contains at least 2 points; a plane contains at least…

Through any 2 points there is one line.

through any 3 points there is at least 1 plane and through an…

If 2 points are in a plane, then the line that contains them…

Postulate 5

A line contains at least 2 points; a plane contains at least…

Postulate 6

Through any 2 points there is one line.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Corresponding Angles Postulate

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

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

On AB is a given plane, choose any point O between A and B. C…

If m is parallel to n with a transversal intersecting both, t…

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Angel Addition Postulate

A line has at least 2 points; a plane…

The points on a line can be paired with real numbers so that…

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

If point B is between angle AOC, AOB+BOC=AOC ; If angle AOC i…

A line has at least 2 points; a plane has at least 3 points (…

Ruler Postulate

The points on a line can be paired with real numbers so that…

Segment Addition Postulate

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

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Parallel Postulate

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

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

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

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

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 m<RSP + m<PST = m<RST

The measure of a minor arc is ________…

Arc Addition Postulate

The measure of the inscribed angle is…

If 2 inscribed angles intercept the sa…

congruent

the measure of an arc formed by 2 adjacent arcs is the sum of…

half

congruent

The measure of a minor arc is ________…

congruent

Arc Addition Postulate

the measure of an arc formed by 2 adjacent arcs is the sum of…

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

What is the difference between a postu…

Definition of Congruence

Segment Addition Postulate

Angle Addition Postulate

A postulate is something that cannot be proven.

if angles have equal measures, then they're congruent

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

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

What is the difference between a postu…

A postulate is something that cannot be proven.

Definition of Congruence

if angles have equal measures, then they're congruent

Postulate 1

Postulate 2

Postulate 3

Postulate 4

- Ruler Postulate... -points on a line can be paired w the real…

-if B is bw A and C, then... AB + BC = AC

-protractor postulate... -match rays w real numbers on a protrac…

-Angle Addition Postulate... -if point B lies in interior of an…

Postulate 1

- Ruler Postulate... -points on a line can be paired w the real…

Postulate 2

-if B is bw A and C, then... AB + BC = AC

Postulate 2/Segment Addition Postulate

congruent

congruent segments

midpoint of a segment

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

the term used to describe two objects with the same size and…

segments that have equal lengths

the point that divides a segment into two congruent segments

Postulate 2/Segment Addition Postulate

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

congruent

the term used to describe two objects with the same size and…

Theorem 9-1

Corollary (of Theorem 9-1)

Theorem 9-2

postulate 16

If a line is tangent to a circle, then the line is perpendicu…

Tangents to a circle from a point are congruent.

If a line in the plane of a circle is perpendicular to a radi…

measure of the arc formed by two adjacent arcs is the sum of…

Theorem 9-1

If a line is tangent to a circle, then the line is perpendicu…

Corollary (of Theorem 9-1)

Tangents to a circle from a point are congruent.