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Study sets matching "properties postulates"

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Study sets matching "properties postulates"

8 terms
Postulates & Properties
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…
9 terms
Properties & Postulates
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
7 terms
Properties and Postulates
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.
15 terms
Postulates and Properties
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.
properties and postulates
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
11 terms
Properties & Postulates
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…
8 terms
Postulates + Properties
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…
11 terms
properties&postulates
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.
12 terms
Properties&Postulates
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
12 terms
Postulates/Properties
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
15 terms
Postulates/Properties
Line Segment Extension Postulate
The Distance Assignment Postulate
The Segment Existence Postulate
Angle Measure Assignment Postulate
...
...
...
...
Line Segment Extension Postulate
...
The Distance Assignment Postulate
...
11 terms
Properties & Postulates
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.
16 terms
postulates/properties
reflexive property
symmetric property
transitive property
addition property
a = a
if a = b, then b = a
if a = b, and b = c, then a = c
if a = b, then a + c = b + c
reflexive property
a = a
symmetric property
if a = b, then b = a
11 terms
Properties & Postulates
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.
11 terms
Properties & Postulates
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…
11 terms
Postulates and properties
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler postulate
Segment addition postulate
Protractor postualte
Angle addtion postulate
Postulate 1
Ruler postulate
Postulate 2
Segment addition postulate
21 terms
Postulates/Properties
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…
15 terms
Properties and Postulates
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
Properties and Postulates
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
19 terms
Properties and Postulates
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
9 terms
properties and postulates
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…
11 terms
Properties and postulates
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.
15 terms
Properties and postulates
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
24 terms
Properties and Postulates
Commutative of Addition
Commutative of Multiplication
Associative of Addition
Associative of Multiplication
a+b = b+a
ab=ba
(a+b) +c = a+(b+c)
(ab)c=a(bc)
Commutative of Addition
a+b = b+a
Commutative of Multiplication
ab=ba
10 terms
Postulates and Properties
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.
14 terms
Properties and Postulates
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
11 terms
Properties and Postulates
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
34 terms
Properties and Postulates
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.
33 terms
Properties and Postulates
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.
34 terms
Properties and Postulates
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.
Postulates and Properties
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.
18 terms
Postulates and Properties
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
34 terms
Properties and Postulates
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.
12 terms
Postulates and Properties
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.
21 terms
properties and postulates
Addition property of equality
Angle addition postulate
Associative property of addition
associative property of multiplication
...
...
...
...
Addition property of equality
...
Angle addition postulate
...
16 terms
Properties and Postulates
Addition Property
Multiplication Property
Subtraction Property
Division Property
If a=b then a+c = b+c
If a=b then ac = bc
If a=b then a-c = b-c
If a=b then a/c = b/c
Addition Property
If a=b then a+c = b+c
Multiplication Property
If a=b then ac = bc
17 terms
Properties and postulates
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
8 terms
Postulates and properties
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…
11 terms
Properties and Postulates
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.
15 terms
Properties and Postulates
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
14 terms
Properties and Postulates
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
21 terms
Postulates and properties
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
12 terms
Properties and Postulates
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
11 terms
Properties and Postulates
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.
8 terms
Properties and Postulates
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…
11 terms
Properties and Postulates
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.
15 terms
Postulates and Properties
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…
12 terms
Properties and Postulates
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
Postulates and Properties
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.
13 terms
Postulates and Properties
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=…
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