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Study sets matching "geometry postulates proofs"

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Study sets matching "geometry postulates proofs"

10 terms
JJ Geometry Postulates (proofs)
Ruler Postulate 1
Segment addition postulate 2
Protractor Postulate 3
Postulate 5
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 then B is between A…
ConsiderOB and a point A on one side of OB. The Rays of the f…
Through any two points there exists exactly one line
Ruler Postulate 1
The points on a line can be matched one to one with the real…
Segment addition postulate 2
If B is between A and C, then AB + BC=AC then B is between A…
38 terms
Theorems and Postulates for Geometry Proofs
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
60 terms
Geometry Postulates, Proofs, etc
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,…
Consider ray OB and a point A on one side of of ray OB. The r…
If P is in the interior of angle of RST, then the measure of…
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,…
20 terms
Geometry proofs and postulates
deff of parellelogram
property of parellelogram
property of parellelogram
property of parellelogram
a quad with 2 sets of // sides
opp sides congruent
opp angles congruent
same side angles are supplementary
deff of parellelogram
a quad with 2 sets of // sides
property of parellelogram
opp sides congruent
19 terms
Geometry Postulates and Proofs
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any 2 points is exactly 1 line.
Through any 3 noncollinear points, there is exactly one plane.
A line contains at least 2 points.
A plane contains at least 3 noncollinear points.
Postulate 2.1
Through any 2 points is exactly 1 line.
Postulate 2.2
Through any 3 noncollinear points, there is exactly one plane.
18 terms
Geometry: Postulates and Paragraph proofs
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…
45 terms
Postulates & Theorems for Proofs (Geometry)
segment addition postulate (SAP)
angle addition postulate (AAP)
addition property of equality
subtraction property of equality
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
Angles can be added together if they are adjacent
Adding a value to each side of an equation... if a=b, then a+c=b+c
subtracting a value from each side of an equation ... if a=b the…
segment addition postulate (SAP)
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
angle addition postulate (AAP)
Angles can be added together if they are adjacent
21 terms
Postulates and Proofs geometry
Definition of a midpoint
Segment addition postulate
Midpoint theorem
Addition
AM = MB
AB + BC = AC
If M is the midpoint of segment AB then AM = 1/2AB
Add equal amounts to both sides of an equation
Definition of a midpoint
AM = MB
Segment addition postulate
AB + BC = AC
9 terms
Geometry Postulates, Proofs, & 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, then a/c=b/c c is ALMOST equal to
Addition Property of Equality
if a=b, then a+c=b+c
Subtraction Property of Equality
if a=b, then a-c=b-c
11 terms
Geometry Postulates & Proofs
2.1
2.2
2.3
2.4
through any 2 points, there is exactly 1 line
through any 3 noncollinear points, there is exactly 1 plane
a line contains at least 2 points
a plane contains at least 3 noncollinear points
2.1
through any 2 points, there is exactly 1 line
2.2
through any 3 noncollinear points, there is exactly 1 plane
24 terms
Geometry Proofs: Definitions and Postulates
Vertical Angles Congruence Theorem
Linear Pair Postulate
Congruent Supplements Theorem
Congruent Complements Theorem
Vertical Angles are Congruent.
If two angles form a linear pair, then they are supplementary.
If two angles are supplementary to the same angle (or to cong…
If two angles are complementary to the same angle (or to cong…
Vertical Angles Congruence Theorem
Vertical Angles are Congruent.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
41 terms
Geometry Proofs, Postulates, and Theorems
If B is between A & C then AB + BC =AC
If two angles have the same measuremen…
If the angles are congruent two angles…
If a point, X, is in the interior of <…
segment addition postulate
definition of congruent angles
definition of congruent angles
angle addition postulate
If B is between A & C then AB + BC =AC
segment addition postulate
If two angles have the same measuremen…
definition of congruent angles
139 terms
Geometry Postulates and Definitions (For Proofs)
1-1
1-2
1-3
1-4
Through any two points there is exactly one line.
If two distinct lines intersect, then they intersect in exact…
If two distinct planes intersect, then they intersect in exac…
Through any three non-collinear points there is exactly one p…
1-1
Through any two points there is exactly one line.
1-2
If two distinct lines intersect, then they intersect in exact…
43 terms
Geometry Proofs - Postulates and Theorems
Segment Addition postulate
Angle Addition postulate
Linear Pair postulate
Definition of Congruence
If M is between A and B, then AM+MB=AB.
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
If two angles form a linear paire, then they are supplementary.
If measures are equal, then parts are congruent.
Segment Addition postulate
If M is between A and B, then AM+MB=AB.
Angle Addition postulate
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
38 terms
Geometry Postulates, Proofs, and Theorems
Ruler Postulate
Segment Addition Postulate
Protector Postulate
Angle Addition Postulate
AB = distance between endpoints
AB+BC=AC if B is between A and C
Ruler Postulate for Angles
Segment Addition Postulate for Angles
Ruler Postulate
AB = distance between endpoints
Segment Addition Postulate
AB+BC=AC if B is between A and C
16 terms
Geometry Postulates and Algebraic Proofs
2.1
2.2
2.3
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
2.1
Through any two points, there is exactly one line.
2.2
Through any three noncollinear points, there is exactly one p…
7 terms
Geometry Postulates & Proofs
Addition/Subtraction Postulate
Multiplication Postulate
Distributive Property
Substitution Property
if A=B and C=D, then A+C = B+D......(A-C = B-D)
if A=B, then AC = BC
A(B+C) = AB + AC
if A=B, then "A" is able to replace "B" in any equation
Addition/Subtraction Postulate
if A=B and C=D, then A+C = B+D......(A-C = B-D)
Multiplication Postulate
if A=B, then AC = BC
21 terms
Geometry proofs and postulates
Subtraction property
Addition 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 0 then a/c=b/c
Subtraction property
If a =b then a-c=b-c
Addition property
If a=b then a+c=b+c
23 terms
Geometry Proofs/Postulates/Definitions
Ruler Postulate(1)
Ruler Postulate(2)
Segment Addition Postulate
Protractor Postulate
The points on a line can be paired with real numbers in such…
Once a coordinate system has been chosen in this way, the dis…
If B is between A and C, then AB+BC=AC
Name the origin of a protractor, and create and to find a cer…
Ruler Postulate(1)
The points on a line can be paired with real numbers in such…
Ruler Postulate(2)
Once a coordinate system has been chosen in this way, the dis…
26 terms
Geometry Proofs and Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be put into a one-to-one corresponde…
If B is between A and C, then AB + BC = AC.
Given line AB and a point O on line AB, all rays that can be…
If S is in the interior of angle PQR, then the measure of ang…
Ruler Postulate
The points on a line can be put into a one-to-one corresponde…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
8 terms
Geometry- proofs and postulates vocab
Proof
Postulate
Inductive reasoning
Conjecture
A logical argument that shows a statement to be true
A rule that is ... excepted without proof
And argument that goes from a specific statement to a general…
A unproven statement that is based on observation
Proof
A logical argument that shows a statement to be true
Postulate
A rule that is ... excepted without proof
22 terms
Postulates, Theorems, Proofs - Geometry
Ruler Postulate
Segment Addition Postulate
Postulate
Protractor 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.
A rule accepted without proof
An angle can be measured from 0 to 180
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:postulates and Proofs
Postulate
Theorem
Postulate 2.1
Postulate 2.2
A statement that is accepted as true without proof.
Once a statement has been proven it is called a ________.
Through any two points, there is exactly one line.
Through any three non-collinear points, there is exactly one…
Postulate
A statement that is accepted as true without proof.
Theorem
Once a statement has been proven it is called a ________.
30 terms
geometry proofs / postulates
2.1
2.2
2.3
2.4
through any 2 points, there is exactly one line
through any 3 non collinear points, there is exactly one 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 one line
2.2
through any 3 non collinear points, there is exactly one plane
16 terms
Geometry postulates/proofs
Postulate 2.1 ... (Lines, points, planes)
Postulate 2.2 ... (Lines, points, planes)
Postulate 2.3... (Lines, points, planes)
Postulate 2.4 ... (Lines, points, planes)
Through any two points, there is exactly one line.
Through any three non-collinear points, there is exactly one…
A line contains at least two points.
A plane contains at least three noncollinear points
Postulate 2.1 ... (Lines, points, planes)
Through any two points, there is exactly one line.
Postulate 2.2 ... (Lines, points, planes)
Through any three non-collinear points, there is exactly one…
13 terms
Geometry Proofs and Postulates
Conditional Statements
Converse
Inverse
Contropositive
If then format
Conditional Statement flipped
Opposite of Conditional Statement
Inverse flipped
Conditional Statements
If then format
Converse
Conditional Statement flipped
34 terms
Geometry proofs - postulates/theorems
segment addition postulate
Def: Midpoint of a segment
Def: Bisector of a segment
angle addition postulate
if B is between A and C, then AB + BC = AC
The point that divides the segment into two congruent segments
A line, segment, ray, or plane that intersects the segment at…
If point B lies in the interior of <AOC, then m<AOB + m<BOC =…
segment addition postulate
if B is between A and C, then AB + BC = AC
Def: Midpoint of a segment
The point that divides the segment into two congruent segments
18 terms
postulates and proofs: geometry
39 terms
Geometry Proofs, postulates, and Theorems
Postulate or axion
Postulate 2.1
Postulate 2.2
Postulate 2.3
A statement that is accepted as true without proof
Through any two distinct points there exists only 1 line
Though any 2 distinct points there exists exactly 1 plane
A line contains at least 2 points
Postulate or axion
A statement that is accepted as true without proof
Postulate 2.1
Through any two distinct points there exists only 1 line
10 terms
Geometry Proofs and Postulates
Subtraction Property
Addition Property
Division Property
Multiplication Property
If a=b,... Then a-c= b-c
If a=b, ... Then a+c=b+c
If a=b... Then a/b=b/c; c≠0
If a=b... Then ac=bc
Subtraction Property
If a=b,... Then a-c= b-c
Addition Property
If a=b, ... Then a+c=b+c
25 terms
Geometry Theorems Postulates and Proofs
Slopes of parallel lines
Parallel Postulate
Slopes of Perpendicular Lines
Symmetric Property
If 2 nonvertical lines are parallel then their slopes are equ…
Through a point not on a line, there is ONLY ONE parallel to…
If 2 nonvertical lines are perpendicular, then the product of…
If a=b then b=a
Slopes of parallel lines
If 2 nonvertical lines are parallel then their slopes are equ…
Parallel Postulate
Through a point not on a line, there is ONLY ONE parallel to…
8 terms
Postulates and Theorems Geometry Proofs
Ruler Postulate
Protractor Postulate
Angle Addition Postulate
Segment Addition Postulate
On a number line, every point can be paired with a number and…
Given line AB and a point O on line AB. Consider rays OA and…
The angle addition postulate states that if B is in the inter…
If a point B lies on a line segment , then . That is, the dis…
Ruler Postulate
On a number line, every point can be paired with a number and…
Protractor Postulate
Given line AB and a point O on line AB. Consider rays OA and…
33 terms
Geometry Proofs Theorems and postulates
Triangle Angle-Sum Theorem
Exterior angle Theorem
Triangle Angle Sum Corollaries
Definition of Congruent Polygons
The sum of the measures of the angles of a triangle is 180
The measure of an exterior angle of a triangle is equal to th…
The acute angles of a right triangle are complementary... There…
Two polygons are congruent if and only if their corresponding…
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180
Exterior angle Theorem
The measure of an exterior angle of a triangle is equal to th…
Geometry Postulates and Properties (Proofs)
Conditional statements
Addition Property of Equality
Multiplication Property of Equality
Division Property of Equality
if-then statements with a hypothesis and a conclusion
If a = b, then a + c = b + c
If a = b, then ac = bc
If a = b, then a/c=b/c, if C≠0
Conditional statements
if-then statements with a hypothesis and a conclusion
Addition Property of Equality
If a = b, then a + c = b + c
44 terms
Geometry PROOFS: Theorems and Postulates
Segment Addition Postulate (SAP)
VAT
Linear Pair Thm
AAP
AB + BC = AC
Two angles are vertical iff their sides form opposite rays
Two adjacent angles form a linear pair iff their non-common s…
Angle Addition Postulate states that if a point S lies in the…
Segment Addition Postulate (SAP)
AB + BC = AC
VAT
Two angles are vertical iff their sides form opposite rays
5 terms
Geometry Theorems, Postulates, and Proofs
Conditional Statement
Converse
Inverse
Contraposistive
A logical statement that has two parts; a hypothesis, and a c…
A conditional statement that switches the places of the hypot…
When the hypothesis and conclusion of a conditional statement…
When the hypothesis and conclusion of a conditional statement…
Conditional Statement
A logical statement that has two parts; a hypothesis, and a c…
Converse
A conditional statement that switches the places of the hypot…
27 terms
GEOMETRY PROOFS POSTULATES AND THEOREMS
Alternate Interior Angles Theorem
Same Side Interior Angles Theorem
Alternate Exterior Angles Theorem
Same Side Exterior Angles Theorem
If 2 parallel lines are intersected by a transversal, then al…
If 2 parallel lines are cut by a transversal, then same side…
If 2 parallel lines are cut by a transversal, the alternate e…
If 2 parallel lines are are cut by a transversal, the same si…
Alternate Interior Angles Theorem
If 2 parallel lines are intersected by a transversal, then al…
Same Side Interior Angles Theorem
If 2 parallel lines are cut by a transversal, then same side…
45 terms
Postulates & Theorems for Proofs (Geometry)
segment addition postulate (SAP)
angle addition postulate (AAP)
addition property of equality
subtraction property of equality
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
Angles can be added together if they are adjacent
Adding a value to each side of an equation... if a=b, then a+c=b+c
subtracting a value from each side of an equation ... if a=b the…
segment addition postulate (SAP)
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
angle addition postulate (AAP)
Angles can be added together if they are adjacent
43 terms
Geometry Proofs - Postulates and Theorems
Segment Addition postulate
Angle Addition postulate
Linear Pair postulate
Definition of Congruence
If M is between A and B, then AM+MB=AB.
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
If two angles form a linear paire, then they are supplementary.
If measures are equal, then parts are congruent.
Segment Addition postulate
If M is between A and B, then AM+MB=AB.
Angle Addition postulate
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
15 terms
Geometry Proofs, Theorems, and Postulates
Corresponding Angle Postulate
Alternate Interior Angle Postulate
Alternate Exterior Angle Postulate
Same-Side Consecutive Interior Angles…
If 2 // lines are cut by a transversal then the corresponding…
If 2 // lines are cut by a transversal then all alternate int…
If 2 angles are cut by a transversal then all alternate exter…
If 2 parallel lines are cut by a transversal then same side i…
Corresponding Angle Postulate
If 2 // lines are cut by a transversal then the corresponding…
Alternate Interior Angle Postulate
If 2 // lines are cut by a transversal then all alternate int…
21 terms
geometry theorems, proofs, postulate
segment addition postulate
reflexive property of congruence
symmetric property of congruence
Transitive property of congruence
if A,B, and C are collinear, then point B is between A and C…
segment AB is congruent to segment AB
if segment AB is congruent to segment CD, the segment CD is c…
if segment AB is congruent to segment CD and CD is congruent…
segment addition postulate
if A,B, and C are collinear, then point B is between A and C…
reflexive property of congruence
segment AB is congruent to segment AB
25 terms
geometry: proof theorems and postulates
adjacent angles
liner pair
vertical angle
addition property of equality
share a common side and vertex
two adjacent angles that have a non common side and forms a l…
two non adjacent angles that are formed by two intersecting l…
if a, b and c are real numbers and a=b the a+c = b+c
adjacent angles
share a common side and vertex
liner pair
two adjacent angles that have a non common side and forms a l…
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
20 terms
Geometry Proofs and Postulates and Parallelograms
Properties of a square
Properties of a rectangle
Properties of a rhombus
Properties of a parallelogram
Both pairs of opposite sides are congruent... Both pairs of oppo…
Both pairs of opposite sides parallel ... Both pairs of opposite…
Both pairs of opposite sides parallel... Both pairs of opposite…
A quadrilateral with both pairs of opposite sides congruent... B…
Properties of a square
Both pairs of opposite sides are congruent... Both pairs of oppo…
Properties of a rectangle
Both pairs of opposite sides parallel ... Both pairs of opposite…
16 terms
Geometry Theorems/Postulates/Properties for PROOFS
AB = AB
BC = CB
If A = B, and B = C, then A = C
If two lines are perpendicular, then y…
Reflexive Property
Symmetric Property
Transitive Property
Definition of Perpendicular Lines
AB = AB
Reflexive Property
BC = CB
Symmetric Property
31 terms
Geometry Postulate, Proofs, and Theorems
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
For every two points there is one line
Brought every three non collinear points there is one plane
For every line there are at least two points
Through every plain there are at least three points
Postulate 2.1
For every two points there is one line
Postulate 2.2
Brought every three non collinear points there is one plane
23 terms
Geometry Proof Postulates & Properties
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be matched one to one with real numb…
If B is between A and C, then AB + BC = AC
Rays can be matched in ankles from 0 degrees to 180 degrees b…
The measuring of a large angle will be equal to the sum of tw…
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
59 terms
Geometry/ Proof postulates and theroems
Ray
Segment
midpoint
angle
A portion of a line with an endpoint extending infinitely in…
A portion of a line with two endpoints
a point that divides a segment into two equal sections
Two rays that share an endpoint
Ray
A portion of a line with an endpoint extending infinitely in…
Segment
A portion of a line with two endpoints
16 terms
Geometry postulates, theorems and proof
What is a postulate
Postulate: through any two points
Postulate: through any three no collin…
Postulate: two lines intersect in a
A statement that is accepted as true without proof
There is exactly one line
There is exactly one plane
Point (vertex)
What is a postulate
A statement that is accepted as true without proof
Postulate: through any two points
There is exactly one line
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
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