Study sets matching "properties postulates"

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Study sets matching "properties postulates"

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…
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
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
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…
5 terms
properties & postulates
reflexive property of equality
symmetric property of equality
transitive property of equality
equivalence relation
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...
...
...
reflexive property of equality
...
symmetric property of equality
...
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.
Properties&Postulates
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
SUBSTITUTION POSTULATE
a=a Aqunantity is equal to itself
if a=b then b=a
if a=b and b=c,then a=c
A quantity may be substituted for its equal in any statement…
Reflexive Property of Equality
a=a Aqunantity is equal to itself
Symmetric Property of Equality
if a=b then b=a
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.
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…
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
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…
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.
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
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.
properties of postulates
reflexive property
symmetric property
transitive property
multiplication postulate
a=a
a=b then b=a
a=b b=c then a=c
a=b c=d ac=bd
reflexive property
a=a
symmetric property
a=b then b=a
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
21 terms
properties and postulates
Addition property of equality
Angle addition postulate
Associative property of addition
associative property of multiplication
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...
...
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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
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…
Postulates and properties
Reflexive property
Symmetric property
Transitive property
Substitution property
A=a
If a=b then b=a
If a=b and b=c then a=c
If x=y, then x may be replaced by y
Reflexive property
A=a
Symmetric property
If a=b then b=a
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
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
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.
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
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.
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.
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.
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=…
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
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
7 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 on…
Postulate 5
Through any two points there exists exactly one line.
Postulate 6
A line contains at least two points.
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.
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.
7 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 quanti…
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
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.
Properties and postulates
Reflexive property of segment congruence
Symmetric property of segment congruence
Transitive property of segment congrue…
Right angle congruence theorem
For any segment AB, AB=AB
If segment AB= segment CD, then segment CD= AB
If segment AB= segment BC and segment BC= segment CD, then se…
All right angles are congruent
Reflexive property of segment congruence
For any segment AB, AB=AB
Symmetric property of segment congruence
If segment AB= segment CD, then segment CD= AB
Properties and Postulates
Reflexive property
Symmetric property
Addition postulate
Subtraction postulate
A quantity is congruent (equal) to itself
If A=B, then B=A
If equal quantities are added to equal quantities then the su…
If equal quantities are subtracted from equal quantities than…
Reflexive property
A quantity is congruent (equal) to itself
Symmetric property
If A=B, then B=A
7 terms
Postulates and Properties
2.1
2.2
2.3
2.4
Through any 2 points there is exactly 1 line
Through any 3 non collinear points there is exactly 1 plane
A line contains at least 2 points
A plane contains at least 3 non collinear points
2.1
Through any 2 points there is exactly 1 line
2.2
Through any 3 non collinear points there is exactly 1 plane
18 terms
Properties and Postulates
Conditional
Converse
Counter-example
Biconditional
Is an if then statement that contains two parts. (Hypothesis…
Of a conditional switches the hypothesis and the conclusion
When the hypothesis is true, and the conclusion is false
When a conditional and it's converse are true, you can combin…
Conditional
Is an if then statement that contains two parts. (Hypothesis…
Converse
Of a conditional switches the hypothesis and the conclusion
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
5 terms
properties and postulates
Reflective 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 a=c, Quantities equal to the same quantity a…
A quantity may be substituted for its equal in any statement…
Reflective 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
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.
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 or…
*If a=b, and b=c, then a=c; ... *Qualities equal to the same qua…
*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 or…
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.
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 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.
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