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Vertical Angles

Linear Pair Postulate

Triangle Sum Theorem

Definition of Complementary

Vertical Angles are congruent

Angles that forma a linear pair are supplementary

the sum of the interior angles of a triangle is 180 degrees

two angles whose measures add to 90 degrees

Vertical Angles

Vertical Angles are congruent

Linear Pair Postulate

Angles that forma a linear pair are supplementary

Ruler Postulate

Segment 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, then AB+BC=AC.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

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

Ruler Postulate

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

Segment Addition Postulate

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

Addition Property

Subtraction Property

Substitution Property

Reflexive Property

You can add EQUAL things to both sides of an EQUATION... "If a =…

You can subtract EQUAL things from both sides of an EQUATION…

If two number are EQUAL, then they can be substituted for one…

Any number equals itself

Addition Property

You can add EQUAL things to both sides of an EQUATION... "If a =…

Subtraction Property

You can subtract EQUAL things from both sides of an EQUATION…

Reflexive Property

Symmetric Property

Transitive Property

Distributive Property

A quantity is equal to itself. ... ex. a = a

Ex. if DE=FG then FG=DE

If A=B and B=C then A=C

If a(b+c) then ab+ac

Reflexive Property

A quantity is equal to itself. ... ex. a = a

Symmetric Property

Ex. if DE=FG then FG=DE

Vertical Angles

Linear Pair Postulate

Triangle Sum Theorem

Definition of Complementary

Vertical Angles are congruent

Angles that forma a linear pair are supplementary

the sum of the interior angles of a triangle is 180 degrees

two angles whose measures add to 90 degrees

Vertical Angles

Vertical Angles are congruent

Linear Pair Postulate

Angles that forma a linear pair are supplementary

Reflexive Property

Symmetric Property

Transitive Property

Addition Postulate

A quantity is congruent (equal) to itself. a = a

If a=b, then b=a

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

If equal quantities are added to equal quantities, the sums a…

Reflexive Property

A quantity is congruent (equal) to itself. a = a

Symmetric Property

If a=b, then b=a

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, then a - c = b - c

If a = b, then (a)(c) = (b)(c)

If a = b, c not equal to "zero", then a/c = b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

coordinate midpoint property

segment additive property

angle addition property

linear pair theorem

if B is between A & C,... then AB+BC=AC

if D is on the interior of Angle ABC,... then m Angle ABD + m An…

if two angles form a linear pair,... then the two angles are sup…

coordinate midpoint property

segment additive property

if B is between A & C,... then AB+BC=AC

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, then a - c = b - c.

If a = b, then ac = bc.

If a = b and c ≠ 0, then a/c = b/c.

Addition Property of Equality

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

Subtraction Property of Equality

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

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, then a-c=b-c

If a=b, then a•c=b•c

If a=b and c≠0, then a/c=b/c

Addition property of equality

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

Subtraction property of equality

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

Define: Reflexive Property

Define:Symmetric Property

Define:Transitive Property

Define:Substitution Property

A quantity is equal to itself. Example: ab=ab

A quantity may be expressed in either order . Example: If a=b…

If two quantities are equal to the same quantity then they ar…

A quantity may be substituted for its equal in any expression…

Define: Reflexive Property

A quantity is equal to itself. Example: ab=ab

Define:Symmetric Property

A quantity may be expressed in either order . Example: If a=b…

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

A quantity is congruent (equal) to itself. a = a

If a=b, then b=a... A quantity may be expressed in either order

If AB = CD, and CD = EF, then AB = E... If two quantities are eq…

if a=b, then a may be replaced by b and b may be replaced by…

Reflexive Property

A quantity is congruent (equal) to itself. a = a

Symmetric Property

If a=b, then b=a... A quantity may be expressed in either order

Through any ___ points, there is/are e…

If ___ distinct lines intersect, the i…

If ___ distinct planes intersect, then…

Through any _____ non collinear point(…

two, one

two, one

two, one

three, one

Through any ___ points, there is/are e…

two, one

If ___ distinct lines intersect, the i…

two, one

Addition Property

Subtraction Property

Multiplication Property

Division Property

You can add EQUAL things to both sides of an EQUATION... "If a =…

You can subtract EQUAL things from both sides of an EQUATION…

You can multiply both sides of the EQUATION by the EQUAL things

You can divide both sides of an EQUATION by EQUAL things long…

Addition Property

You can add EQUAL things to both sides of an EQUATION... "If a =…

Subtraction Property

You can subtract EQUAL things from both sides of an EQUATION…

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

the distance between points A and B, written as AB, is the ab…

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

the measure of ∠AOB, which can be written as m∠AOB, is equal…

if b is in the interior of ∠COA, then m∠COA is equal to the s…

ruler postulate

the distance between points A and B, written as AB, is the ab…

segment addition postulate

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

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

The property that states that if you add the same number to b…

States that when both sides of an equation have the same numb…

states that if you multiply both sides of an equation by the…

states that if you divide both sides of an equation by the sa…

Addition Property of Equality

The property that states that if you add the same number to b…

Subtraction Property of Equality

States that when both sides of an equation have the same numb…

inductive reasoning

counterexample

conjecture

truth value

uses numbers or specific examples to arrive at a plausible ge…

An example which disproves a proposition.

is an educated guess based on known information

the truth or falsity of a statement

inductive reasoning

uses numbers or specific examples to arrive at a plausible ge…

counterexample

An example which disproves a proposition.

Definition of Congruent Segments

Definition of Congruent Angles

Segment Addition Postulate

Definition of Midpoint

If AB≅XY Then AB=XY

If ∠1≅∠3 Then m∠1=m∠3

I B is between A and C Then AB+BC_AC

If M is the midpoint of AB Then AM = MB

Definition of Congruent Segments

If AB≅XY Then AB=XY

Definition of Congruent Angles

If ∠1≅∠3 Then m∠1=m∠3

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Reflexive Property of Congruence

If there is a quantity, then it is equal to itself

If a=b, then b=a

If a=b and b=c, then a=c

If there is a quantity, then it is congruent to itself

Reflexive Property of Equality

If there is a quantity, then it is equal to itself

Symmetric Property of Equality

If a=b, then b=a

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, then a - c = b - c

if a=b, then ac=bc

If a=b and c≠0 then a/c = b/c.

Addition Property of Equality

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

Subtraction Property of Equality

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

Subtraction Postulate

Multiplication Postulate

Division Postulate

Substitution Postulate

If equal quantities are subtracted from equal quantities, the…

If equal quantities are multiplied by equal quantities, the p…

If equal quantities are divided by equal nonzero quantities,…

A quantity may be substituted for its equal in any expression.

Subtraction Postulate

If equal quantities are subtracted from equal quantities, the…

Multiplication Postulate

If equal quantities are multiplied by equal quantities, the p…

Segment Addition Postulate

Angle Addition Postulate

Two-Point Postulate

Line-Point Postulate

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

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

Through any two points, there is exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

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

Ruler Postulate

Segment 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, then AB+BC=AC.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

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

Ruler Postulate

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

Segment Addition Postulate

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

Transitive Property (angles)

Transitive Property (segments)

Substitution Property

Angle-Side-Angle Postulate

If angles are congruent to the same angle, then they are cong…

If segments are congruent to the same segment, then they are…

A value may be substituted for its equal in any expression

If two angles and the included side are congruent to the corr…

Transitive Property (angles)

If angles are congruent to the same angle, then they are cong…

Transitive Property (segments)

If segments are congruent to the same segment, then they are…

reflexive propety

symmetric property

transitive property

addition postulate

a quantity is congruent to itself (a=a)

If a=b, then b=a

if a=b and b=c, then a=c

if equal quantities are added to equal quantities, the sums a…

reflexive propety

a quantity is congruent to itself (a=a)

symmetric property

If a=b, then b=a

Polygon Angle Sum Theorem

Polygon Exterior Angle Sum Theorem

Theorem 6.2.1 (Opp. sides parallelogra…

Theorem 6.2.2 (Opp. angles parallelogr…

The sum of the interior angle measures of a convex polygon wi…

The sum of the exterior angle measures, one angle at each ver…

If a quadrilateral is a parallelogram, then its opposite side…

If a quadrilateral is a parallelogram, then its opposite angl…

Polygon Angle Sum Theorem

The sum of the interior angle measures of a convex polygon wi…

Polygon Exterior Angle Sum Theorem

The sum of the exterior angle measures, one angle at each ver…

Perpendicular lines

postulate 5

Postulate 6

Postulate 7

when two lines intersect to form a right angle

Through any two points there exists exactly one lime

A line contains at least two points

If two lines intersect, then their intersection is exactly on…

Perpendicular lines

when two lines intersect to form a right angle

postulate 5

Through any two points there exists exactly one lime

adjacent angle

angles form a linear pair if

two angles form a pair of vertical ang…

postulate 1

two angles in the same plane that share a common vertex and r…

they are adjacent angles and their non-common rays are opposi…

the rays forming one are the opposite rays of the other

if two angles form a linear pair they are supplementary

adjacent angle

two angles in the same plane that share a common vertex and r…

angles form a linear pair if

they are adjacent angles and their non-common rays are opposi…

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, then a-c=b-c

If a=b, then ac=bc

If a=b and c does not equal 0, then a/c=b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

Segment Addition Postulate

Angle Addition Postulate

Postulate 5

Postulate 6

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

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

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.

Angle Addition Postulate

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

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Addition Property

The distance from one endpoint to the other is the sum of the…

Putting two angles whose measures create a new angle that is…

Angles that are straight, therefore they MUST be supplementary

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

Segment Addition Postulate

The distance from one endpoint to the other is the sum of the…

Angle Addition Postulate

Putting two angles whose measures create a new angle that is…

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…

Given two points...

Ruler Postulate

On a ray, there is exactly one point t…

If M is the midpoint of segment AB,

there is a unique distance between them.

There is a one to one correspondence between the two points o…

a given distance from the endpoint of the ray.

then 2AM = AB and AM = 1/2 AB.

Given two points...

there is a unique distance between them.

Ruler Postulate

There is a one to one correspondence between the two points o…

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, they intersect at exactly on…

If two distinct planes intersect, they intersect at exactly o…

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

Postulate 1-1

Through any two points, there is exactly one line.

Postulate 1-2

If two distinct lines intersect, they intersect at exactly on…

reflexive property

symmetric property

transitive property

postulate

a quantity is equal to itself

an equation may be expressed in either order

if quantities are equal to the same quantity, they are equal…

a statement whose truth is accepted without proof

reflexive property

a quantity is equal to itself

symmetric property

an equation may be expressed in either order

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Perpendicular Lines

A=A

A=B... B=A

If A=B & B=C, then A=C

Lines that intersect and form right angles

Reflexive Property of Equality

A=A

Symmetric Property of Equality

A=B... B=A

Postulate 5

Postulate 6

Postulate 8

Postulate 9

Through any 2 points there exists exactly one line

A line contains at least 2 points

Through any 3 non-collinear points there exists exactly one p…

A plane contains at least 3 noncollinear points

Postulate 5

Through any 2 points there exists exactly one line

Postulate 6

A line contains at least 2 points

perpindicular lines

complementary angles

vertical angles

addition property

two lines that intersect to form right angles

pairs of angles whose measures add up to 90 degrees

pair of non-adjacent angles formed by intersecting lines

if a=b and c=d then a+c = b+d

perpindicular lines

two lines that intersect to form right angles

complementary angles

pairs of angles whose measures add up to 90 degrees

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The point on a line can be matched one to one with real numbers

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

m∠OAB is equal to the absolute value of the difference betwee…

If P id in the interior of ∠RST, then m∠RST = m∠RSP + ∠

Ruler Postulate

The point on a line can be matched one to one with real numbers

Segment Addition Postulate

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

Reflexive Property

Symmetric Property

Transitive Property

Addition Postulate

A quantity is congruent to itself, a=a

If b=a then a=b

If a=b and b=c then a=c

If equal quantities are added to equal quantities, then the s…

Reflexive Property

A quantity is congruent to itself, a=a

Symmetric Property

If b=a then a=b

Addition Property

Subtraction Property

Multiplication Property

Division Property

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

if a = b, then a - c = b - c

if a = b, then ac = bc

if a = b and c ≠ 0, then a ÷ c = b ÷ c

Addition Property

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

Subtraction Property

if a = b, then a - c = b - c

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 then a-c=b-c

If a=b then ac=bc

If a=b and c is not equal to zero then a/c=b/c

Addition property of equality

If a=b then a+c=b+c

Subtraction property of equality

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

supplement theorem

SAP

point-line postulate

point-plane theorem

supplements of congruent angles (or the same angle) are congr…

if AB = CD, then AB + BC = BC + CD

given any two points, there exists exactly one line containin…

given any three non-collinear points there exists exactly one…

supplement theorem

supplements of congruent angles (or the same angle) are congr…

SAP

if AB = CD, then AB + BC = BC + CD

Cross Product Property of proportions

Reciprocal property of proportions

Switching Property of proportions

Add property of proportions

The product of the extremes equals the product of the means.…

If 2 ratios are equal then their reciprocals are also equal.…

If a/b=c/d, then a/c=b/d

If a/b=c/d, then a+b/b=c+d/d

Cross Product Property of proportions

The product of the extremes equals the product of the means.…

Reciprocal property of proportions

If 2 ratios are equal then their reciprocals are also equal.…

Definition of Midpoint

Definition of Bisector

Definition of Angle Bisector

Definition of Perpendicular

The point halfway between two given points.

A line segment, line, or plane that divides a geometric figur…

A line or ray that divides an angle in half.

Two lines bisect and form a 90 degree angle.

Definition of Midpoint

The point halfway between two given points.

Definition of Bisector

A line segment, line, or plane that divides a geometric figur…

Corresponding Angles Converse Postulate

Alternate Interior Angles Converse The…

Alternate Exterior Angles Converse The…

Consecutive Interior Angles Converse T…

if two lines are cut by a transversal so that corresponding a…

if two lines are cut by a transversal so that alternate inter…

if two lines are cut by a transversal so that alternate exter…

if two lines are cut by a transversal so that the consecutive…

Corresponding Angles Converse Postulate

if two lines are cut by a transversal so that corresponding a…

Alternate Interior Angles Converse The…

if two lines are cut by a transversal so that alternate inter…

Addition property

subtraction property

multiplication property

division property

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

if a=b, then a-c=b-c

if a=b, then a**c=b**c

if a=b and c does not equal 0, then a/c = b/c

Addition property

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

subtraction property

if a=b, then a-c=b-c

Addition Property

Subtraction Property

Multiplication Property

Division Property

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

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

If a=b, then a**c = b**c

If a=b and c is not equal to 0, then a/c = b/c

Addition Property

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

Subtraction Property

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