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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

Theorem 9-1

Corollary to Theorem 9-1

Theorem 9-2 (converse of theorem 9-1)

Arc Addition Postulate

If a line is tangent to a circle, then it is perpendicular to…

Tangent segments to a circle from an external point are congr…

If a line is perpendicular to a radius at its outer endpoint,…

One arc plus another arc will equal the total value of the tw…

Theorem 9-1

If a line is tangent to a circle, then it is perpendicular to…

Corollary to Theorem 9-1

Tangent segments to a circle from an external point are congr…

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

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…

*** theorem 9-1 ***

*** corollary to theorem 9-1 ***

*** theorem 9-2 ***

** postulate 16 : arc addition postula…

if a line is tangent to a circle , then the line is perpendic…

tangents to a circle from a point are congruent

if a line of a circle is perpendicular to the radius at its o…

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

*** theorem 9-1 ***

if a line is tangent to a circle , then the line is perpendic…

*** corollary to theorem 9-1 ***

tangents to a circle from a point are congruent

Biconditional Tangent Perpendicular to…

The two tangents to a circle from a po…

Arc Addition Postulate

Congruent minor arcs <=> congruent cen…

A line is tangent to a circle, if and only if the line is per…

...are congruent.

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

In the same circle or in congruent circles, two minor arcs ar…

Biconditional Tangent Perpendicular to…

A line is tangent to a circle, if and only if the line is per…

The two tangents to a circle from a po…

...are congruent.

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

If a line is tangent to a circle then…

Tangents to a circle from one point are

If a line in the plane of a circle is…

The measure of the arc formed by two a…

Perpendicular to the radius drawn to the point of tangency

Congruent

Tangent to the circle

The sum of the measures of these two arcs (arc addition postu…

If a line is tangent to a circle then…

Perpendicular to the radius drawn to the point of tangency

Tangents to a circle from one point 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…

Congruent Circles Theorem

Similar Circles Theorem

Tangent Segments Theorem

Secant Segments Theorem

Two or more circles are congruent if they have the same radiu…

All circles are similar

If two tangents intersect outside of a circle, they are congr…

If two secants intersect outside of a circle, then the produc…

Congruent Circles Theorem

Two or more circles are congruent if they have the same radiu…

Similar Circles Theorem

All circles are similar

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line.

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

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

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

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

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…

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.

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

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

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…

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…

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…

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

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

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…

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

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

Law of Detachment

Law of Syllogism

Properties of Congruence

Vertical Angles Theorem

If a conditional is true and its hypothesis is true, then its…

If p→q and q→r are true statements, then p→r is a true statem…

Reflexive Property: AB≅AB and ∠A≅∠A. Symmetric Property: If A…

Vertical angles are congruent.

Law of Detachment

If a conditional is true and its hypothesis is true, then its…

Law of Syllogism

If p→q and q→r are true statements, then p→r is a true statem…

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Same-Side Interior Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, then alternat…

Corresponding Angles Postulate

If a transversal intersects two parallel lines, then correspo…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

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…

Parallel Lines (||)

Parallel Planes

Skew

Transversal

2 lines that never intersect

2 planes that never intersect

lines which are not coplanar and do not intersect

a line which intersects 2 or more lines

Parallel Lines (||)

2 lines that never intersect

Parallel Planes

2 planes that never intersect

Point

Line

Planes

Collinear

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

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

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

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,…

Theorem 9-1

Corollary 1 to Theorem 9-1

Theorem 9-2

Postulate 16-Arc Addition Postulate

If a line is tangent to a circle, than 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…

The measures of the arc formed by 2 adjacent arcs is the sum…

Theorem 9-1

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

Corollary 1 to Theorem 9-1

Tangents to a circle from a point are congruent.

Theorem 6-1

Theorem 6-2

Theorem 6-3

Theorem 6-4

Opposite sides of a parallelogram are congruent.

Opposite angles of a parallelogram are congruent.

The diagonals of a parallelogram bisect each other.

If three (or more) parallel lines cut off congruent segments…

Theorem 6-1

Opposite sides of a parallelogram are congruent.

Theorem 6-2

Opposite angles of a parallelogram are congruent.

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 angle PQR, then m<PQS + m<SQR = m<…

a2 + b2 = c2

If 2 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 angle PQR, then m<PQS + m<SQR = m<…

Inductive Reasoning

Conjecture

Counterexample

Statement

logic used to reach a conclusion or conjecture

A conclusion that is maybe true or false

example that shows that a conjecture is false

a sentence that can be either True or False

Inductive Reasoning

logic used to reach a conclusion or conjecture

Conjecture

A conclusion that is maybe true or false

Polygons whose corresponding parts are…

The same or equal.

If two angles of one triangle are cong…

If three sides of one triangle are con…

Congruent Polygons

Congruent

Triangle Third Angle Sum Theorem

SSS Congruence Postulate

Polygons whose corresponding parts are…

Congruent Polygons

The same or equal.

Congruent

Postulate 1

Postulate 2

Postulate 3

Postulate 4

"A line, a plane, and space. Each contain an infinite number…

For every 2 points, there exists 1 unique line containing them.

For every 3 noncolinear points, there exists 1 unique plane c…

If 2 points are in a plane, then the line containing them is…

Postulate 1

"A line, a plane, and space. Each contain an infinite number…

Postulate 2

For every 2 points, there exists 1 unique line containing them.

Theorem 6-1: The Exterior Angle Theorem

Theorem 6-2

Theorem 6-3

Corollary 1

The measure of an exterior angle of a triangle is greater tha…

If one side of a triangle is longer than a second side, then…

If one angle of a triangle is larger than a second angle, the…

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

Theorem 6-1: The Exterior Angle Theorem

The measure of an exterior angle of a triangle is greater tha…

Theorem 6-2

If one side of a triangle is longer than a second side, then…

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…

means-extremes product theorem

similar polygons definition

perimeter theorem

3 methods of proving triangles congruent

product of means is equal to the product of extremes

1. corresponding angles are congruent... 2. corresponding sides…

the ratio of the perimeters of any 2 similar polygons equals…

1. AA similarity... 2. SSS similarity... 3. SAS similarity

means-extremes product theorem

product of means is equal to the product of extremes

similar polygons definition

1. corresponding angles are congruent... 2. corresponding sides…

Theorem 4.1 (Angle Sum Theorem)

Theorem 4.2 (Exterior Angles Theorem)

Corollary 4.1

Corollary 4.2

all three angles of a triangle equal 180 degrees

The exterior angle is equal to the sum of the 2 remote interi…

In a right triangle, the 2 acute angles are complementary

A triangle can have at most one right angle or one obtuse angle

Theorem 4.1 (Angle Sum Theorem)

all three angles of a triangle equal 180 degrees

Theorem 4.2 (Exterior Angles Theorem)

The exterior angle is equal to the sum of the 2 remote interi…

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…