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Ruler Postulate

Protractor Postulate

Angle Addition Postulate

Segment Addition Postulate

The distance between two point A and B is denoted by AB.

Given line AB and a point O on line AB. Consider rays OA and…

if B is in the interior of AOC, then. That is, the measure of…

If a point B lies on a line segment , then . That is, the dis…

Ruler Postulate

The distance between two point A and B is denoted by AB.

Protractor Postulate

Given line AB and a point O on line AB. Consider rays OA and…

reflexive property

transitive property

symmetric property

addition postulate

a value is equal to itself

if a=b & b=c, then a=c

if a=b then b=a

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

reflexive property

a value is equal to itself

transitive property

if a=b & b=c, then a=c

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

A quantity is equal to itself.

A quantity may be expressed in any order.

If quantities are equal to the same quantity, then they are e…

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

Reflexive Property of Equality

A quantity is equal to itself.

Symmetric Property of Equality

A quantity may be expressed in any order.

Addition Property of Equality

Division Property of Equality

Reflexive Property of Equality

Transitive Property of Equality

You can add the same number to each side of an equation.

You can divide each side of an equation by the same number.

A value equal to itself (reflection).

If two values are equal to a third value, then they are equal…

Addition Property of Equality

You can add the same number to each side of an equation.

Division Property of Equality

You can divide each side of an equation by the same number.

symmetric

reflexive

transitive

substitution

What property is this?... If m∠1 = m∠2, then m∠2 = m∠1

What property is this?... m∠2 = m∠2

What property is this?... If Ef = GH and GH = IJ, then EF = IJ

What property is this?... If EF = 8 and EF = GH, then GH = 8

symmetric

What property is this?... If m∠1 = m∠2, then m∠2 = m∠1

reflexive

What property is this?... m∠2 = m∠2

the substitution postulate

the partition postulate

the addition postulate

the subtraction postulate

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

A whole is equal to the sum of its parts. A segment and an an…

if a=b and c=d then a+c=b+d. If congruent segments or angles…

if a=b and c=d then a-c=b-d, if equal quantities are subtract…

the substitution postulate

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

the partition postulate

A whole is equal to the sum of its parts. A segment and an an…

Linear Pair postulate

Segment addition postulate

Angle Addition Postulate

Addition Property of equality

If two angles form a linear pair then the angles are suppleme…

If point B is on line segment AC and between point A and C th…

If point D lies in the interior of angle ABC then the measure…

If A,B and C are real numbers and a = b then a + c = b + c

Linear Pair postulate

If two angles form a linear pair then the angles are suppleme…

Segment addition postulate

If point B is on line segment AC and between point A and C th…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

a=b A quantity is equal to itself.

if a=b then b=a A quantity maybe expressed in either order.

if a=b b=c then a=c quantities equal to the same quantity tha…

A quantity may be substitution for its equal in any statement…

Reflexive Property of Equality

a=b A quantity is equal to itself.

Symmetric Property of Equality

if a=b then b=a A quantity maybe expressed in either order.

reflexive property equality

symmetric property of equality

transitive property of equality

substitution postulate

A quantity is equal toitself

An equality may be expressed in either order

quantities equal to the same quantity are equal to each other

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

reflexive property equality

A quantity is equal toitself

symmetric property of equality

An equality may be expressed in either order

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

Every point on a line corresponds to a number... Length=|a-b|

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

Every Ray corresponds to a number, the measure of an angle= |…

If D is inside <ABC then the measure= m<ABD + m<DBC= m<ABC

Ruler postulate

Every point on a line corresponds to a number... Length=|a-b|

Segment addition postulate

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

a=a A quantity is equal to itself.

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

If a=b,b=c, then a=c. Quantities equal to the same quantity a…

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

Reflexive Property of Equality

a=a A quantity is equal to itself.

Symmetric Property of Equality

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

The Substitution Postulate

a=a. A quantity is equal to itself.

If a=b, then b=a. An equality may be expressed in either order.

If a=b & b=c, then a=c. Quantities equal to the same quantity…

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

Reflexive Property of Equality

a=a. A quantity is equal to itself.

Symmetric Property of Equality

If a=b, then b=a. An equality may be expressed in either order.

the substitution postulate

the partition postulate

the addition postulate

the subtraction postulate

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

A whole is equal to the sum of its parts. A segment and an an…

if a=b and c=d then a+c=b+d. If congruent segments or angles…

if a=b and c=d then a-c=b-d, if equal quantities are subtract…

the substitution postulate

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

the partition postulate

A whole is equal to the sum of its parts. A segment and an an…

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. if AB+BC=AC, then B i…

the rays of the form OA can be matched one to one with the re…

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

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. if AB+BC=AC, then B i…

Postulate

Theorem

Reflexive property

Symmetric property

A Statement who proof is accepted without proof

A statement proved by deductive reasoning

A quantity is equal to itself

An equality may be expressed in either order

Postulate

A Statement who proof is accepted without proof

Theorem

A statement proved by deductive reasoning

Transitive property

Symmetric property

Addition Postulate

Partition postulate

If two quantities are equal to the same quantity , they are e…

If a=b then b=a

ac= ab + bc

A whole thing is equal to the sum of its parts

Transitive property

If two quantities are equal to the same quantity , they are e…

Symmetric property

If a=b then b=a

Postulate

Theorem

Reflexive property of equality

Symmetric property of equality

A statement whose truth is accepted without proof

A statement that has to be proven by deductive reasoning

A quantity equals itself

An equality can be expressed in any order

Postulate

A statement whose truth is accepted without proof

Theorem

A statement that has to be proven by deductive reasoning

symmetric property

transitive property

substitution postulate

addition postulate

an equality may be reversed

quantities equal to the the same quantity are equal to each o…

equals can be substituted for each other

if equals are added to equals, their sum is equals

symmetric property

an equality may be reversed

transitive property

quantities equal to the the same quantity are equal to each o…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

The Substitution Postulate

a=a A quantity is equal to itself

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

If a=b, b=c, then a=c. Quantities equal to the same quantity…

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

Reflexive Property of Equality

a=a A quantity is equal to itself

Symmetric Property of Equality

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

Postulate 5

Postulate 6

postulate 7

postulate 8

Through any two points there exist exactly one line.

A line contains at least two points

If two lines intersect then there intersection is exactly one…

Through any 3 noncollinear point there exist exactly 1 point

Postulate 5

Through any two points there exist exactly one line.

Postulate 6

A line contains at least two points

Segment Addition Postulate

Addition Property

Subtraction Property

Multiplication Property

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

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

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

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

Segment Addition Postulate

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

Addition Property

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

Distributive Property

Segment Addition Postulate

Angle Bisector Definition

Angle Bisector Theorem

a(b+c)=ab+bc

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

If BC bisects ABC, then ABD=ABC

If BC bisects ABD, then ABC = 1/2 ABD, CBD = 1/2 ABD

Distributive Property

a(b+c)=ab+bc

Segment Addition Postulate

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

addition property

subtraction property

multiplication property

division property

if equals are added to equals, the results are equal

if equals are subtracted from equals, the results are equal

if equals are multiplied by equals, their products are equal

if equals are divided by nonzero equals, their quotients are…

addition property

if equals are added to equals, the results are equal

subtraction property

if equals are subtracted from equals, the results are equal

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, the a - c = b - c.

If a = b, then ac = bc.

...

Addition Property of Equality

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

Subtraction Property of Equality

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

If a = b, then ac = bc.

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

Addition Property of Equality

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

Subtraction Property of Equality

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

If a = b, then ac = bc.

If one divides both sides of an equation by the same nonzero…

Addition Property of Equality

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

Subtraction Property of Equality

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

a=a A quantity is equal to itself.

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

If a=b, b=c, then a=c. Quantities equal to the same quantity…

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

Reflexive Property of Equality

a=a A quantity is equal to itself.

Symmetric Property of Equality

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

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 times c = b times c

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

If a = b, then ac = bc.

...

Addition Property of Equality

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

Subtraction Property of Equality

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

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line.

A line contains at least two points.

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

Through any three noncollinear points, there exists exactly o…

Postulate 5

Through any two points there exists exactly one line.

Postulate 6

A line contains at least two points.

Postulates

Theorem

The reflexive property of equality

The symmetric property of equality

A statement that we accept its truth without proof

Statements that need to be proven by deductive reasoning

A quantity is equal to itself

Statement of equality can be expressed in any order

Postulates

A statement that we accept its truth without proof

Theorem

Statements that need to be proven by deductive reasoning

Linear addition postulate

Segment addition postulate

Angle addition postulate

Addition property of equality

If 2 angles form a linear paid then the angles are supplement…

If ponit b is on like ac and between ponits a ajs c then ab+b…

If ponit d lies in the interior of angle abc then angke abd+d…

Setting numbers equall to each other ex a+b=b+c

Linear addition postulate

If 2 angles form a linear paid then the angles are supplement…

Segment addition postulate

If ponit b is on like ac and between ponits a ajs c then ab+b…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

a=a A quantity is equal to itself.

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

If a=b, b=c, then c=a Quantities equal to the same quantity a…

A quantity may be substituted for it's equal in any statement…

Reflexive Property of Equality

a=a A quantity is equal to itself.

Symmetric Property of Equality

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

reflexive property of equality

symmetric property of equality

transitive property of equality

substitution postulate

a quantity is equal to itself

statements of equality can be expressed in any orders

...

a quantity can be substituted for its equal in any statement…

reflexive property of equality

a quantity is equal to itself

symmetric property of equality

statements of equality can be expressed in any orders

Postulate

Theorem

Reflexive Property of Equality

Symmetric Property of Equality

A statement whose truth is accepted with out proof

A statement that has to be proven by deductive reasoning

A quantity equals itself

An equality can be expressed in any order

Postulate

A statement whose truth is accepted with out proof

Theorem

A statement that has to be proven by deductive reasoning

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points exists exactly one line

A line contains at least two points

If two lines intersect then their intersection is exactly one…

Through any three points exists exactly one plane

Postulate 5

Through any two points exists exactly one line

Postulate 6

A line contains at least two points

Substitution property

Reflexive property

Transitive property

Symmetric property

If you prove 2 parts are congruent, they can substitute... If x+…

the same part is equal to the same part. AB=AB

If AB=CD and CD=XY then AB=XY

If A=B, then B=A.

Substitution property

If you prove 2 parts are congruent, they can substitute... If x+…

Reflexive property

the same part is equal to the same part. AB=AB

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

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

If a=b, then b=a ... An equality may be expressed in either order.

If a=b and b=c, then a=c... Quantities equal to the same quantit…

If x=y, and y=8, the x=8... A quantity may be substituted for it…

Reflexive Property of Equality

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

Symmetric Property of Equality

If a=b, then b=a ... An equality may be expressed in either order.

the substitution postulate

the partition postulate

the addition postulate

the subtraction postulate

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

A whole is equal to the sum of its parts. A segment and an an…

if a=b and c= d then a+c = b+d. If congruent segments or angl…

if a=b and c=d-d, if equal quantities are subtracted from equ…

the substitution postulate

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

the partition postulate

A whole is equal to the sum of its parts. A segment and an an…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Postulate

a=a A quantity is equal to itself

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

If a=b and b=c, then a=c Quantities equal to the same quantit…

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

Reflexive Property of Equality

a=a A quantity is equal to itself

Symmetric Property of Equality

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

2.1

2.2

2.3

2.4

Through any two points there ja exactly one line

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

A line contains at least two points

A place contains at least three non collinear points

2.1

Through any two points there ja exactly one line

2.2

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

Reflexive property

Symmetric Property

Transitive property

Addition postulate

A quantity is 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 then the su…

Reflexive property

A quantity is equal to itself (a=a)

Symmetric Property

If a=b then b=a

2.1 Two Point Postulate

2.2 Line Point Postulate

2.3 Line Intersection Postulate

2.4 Three Point Postulate

Through any two points, there exists exactly one line.

A line contains at least two points.

If two lines intersect, their intersection is exactly one poi…

Through any three non-collinear points, there exists exactly…

2.1 Two Point Postulate

Through any two points, there exists exactly one line.

2.2 Line Point Postulate

A line contains at least two points.

Ruler Postulate

Segment Addition Postulate (SAP)

Protractor Postulate

Angle Addition Postulate

The measure of any line segment is a unique positive #.

If x is the midpoint of line segment AB an A-x-B, then AX+XB=…

The measure of an angle is a unique positive #.

If point D lies in the interior of angle ABC, then the measur…

Ruler Postulate

The measure of any line segment is a unique positive #.

Segment Addition Postulate (SAP)

If x is the midpoint of line segment AB an A-x-B, then AX+XB=…