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Study sets matching "postulates geometry properties"

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Study sets matching "postulates geometry properties"

17 terms
Geometry postulates, properties, theories
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
31 terms
Geometry Theorems, Postulates, and 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.
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.
18 terms
Geometry Definitions/Postulates/Properties
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…
13 terms
Geometry Properties and Postulates :)
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
Geometry postulates, properties, theories
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
19 terms
Geometry properties and postulates
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
40 terms
Geometry Theorems, 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, 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
25 terms
Geometry Properties, Postulates, and Theorems
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
59 terms
Geometry Postulates, Theorems, 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 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.
35 terms
Geometry Theorems, 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•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
8 terms
Geometry: Properties and Postulates
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…
Geometry Properties and Postulates
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
41 terms
Geometry Postulates and Properties
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
26 terms
Geometry Definitions/Postulates/Properties
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…
27 terms
Geometry Postulates/Theorems/Properties
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…
12 terms
Geometry Properties, Definitions, and Postulates
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…
44 terms
geometry postulates and properties
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.
37 terms
Geometry: Properties, Theorems, & Postulates
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
9 terms
Geometry Properties & Postulates (Definitions)
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
25 terms
2015 Geometry Properties, Postulates, and Theorems
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
48 terms
Geometry Properties and Postulates
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…
31 terms
Geometry Theorems, Postulates, and 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.
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.
29 terms
Geometry Theorems, Postulates, and Properties
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…
6 terms
Geometry Properties and Postulates
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…
27 terms
Geometry Unit 6 Properties, Theorems, & Postulates
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…
50 terms
Geometry postulates/theorems/properties
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
29 terms
Geometry: properties, theorems, postulates
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
Geometry Postulates/Axioms/Properties
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…
18 terms
Geometry Unit 2 Properties, Theorems, & 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, 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
19 terms
Geometry Postulates and Properties
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…
14 terms
Geometry Postulates and Properties
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…
18 terms
Geometry Postulates and Properties
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…
16 terms
Geometry theorems, postulates, and properties
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…
103 terms
Geometry Theorems, Properties, and Postulates
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…
18 terms
Geometry Properties, Postulates and Theorems
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
9 terms
Geometry properties/postulates
addition POE
subtraction POE
symmetric POE
transitive POE
if a=b, then a+c= b+c
if a=b then a-c=b-c
If a=b then b=a
If a = b and b = c, then a = c.
addition POE
if a=b, then a+c= b+c
subtraction POE
if a=b then a-c=b-c
Geometry Postulates, Properties, & Theorems
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
35 terms
Geometry - Postulates, Theorems, & Properties
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
10 terms
Geometry: Definitions, Properties, and Postulates
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
20 terms
Geometry Postulates, Properties, and Theorems
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…
10 terms
Geometry Honors Properties and Postulates
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
26 terms
Geometry Properties, Theorems, and Postulates
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
40 terms
Geometry Theorems, Postulates, and Properties
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
19 terms
Geometry postulates, theorems, 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 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
18 terms
Geometry: Definitions, Postulates, Properties and Theorems
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…
12 terms
Geometry Chapter 8 Postulates, Theorems, and Properties
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.…
24 terms
Geometry Theorems, Properties, and Postulates
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…
18 terms
Postulates, Propertys, and theorems- Geometry
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 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
32 terms
Geometry Theorems/Postulates/Properties
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, 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
11 terms
Geometry~Properties and Postulates
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 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
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