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…
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
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
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.
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
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.
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…
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
geometry postulates/theorems for proofs
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
if a=b then a+c= b+c... you can add something to both sides of a…
if a=b then a-c= b-c... you can subtract something from both sid…
if a=b then a x c = b x c... you can multiply both sides of an e…
if a=b then a/c= b/c... you can divide both side of an equation…
addition property of equality
if a=b then a+c= b+c... you can add something to both sides of a…
subtraction property of equality
if a=b then a-c= b-c... you can subtract something from both sid…
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
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…
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…
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
Geometry Proof Postulates
Parallel Postulate
Segment Addition Postulate
Angle Addition Postulate
Segment Addition Postulate
only one line can be drawn through a given point so that the…
If B is between A and C, then AB+BC=AC
If R is in the interior of <PQS, then <PQR+<RQS=<PQS
Length of pieces of a segment sum to the total length
Parallel Postulate
only one line can be drawn through a given point so that the…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
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
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.
geometry proofs and postulates
isosceles triangle thm
converse of the isosceles triangle thm
perpendicular bisector thm
angle side angle post (asa)
if two sides of a triangle are congruent, then the angles opp…
if two angles of a triangle are congruent, then the sides opp…
points on a perpendicular bisector of a segment are equidista…
if two angles and the included side of the triangle are congr…
isosceles triangle thm
if two sides of a triangle are congruent, then the angles opp…
converse of the isosceles triangle thm
if two angles of a triangle are congruent, then the sides opp…
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 ________.
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
Geometry proofs, postulates, etc
Reflexive property of congruence
Symmetry property of congruence
Transitive property of congruence
Alternate interior angle theorem
when the variable equals itself
If a=b then b=a
if a=b and b=c then a=c
if 2 parallel lines are intersected by a traversal, then alte…
Reflexive property of congruence
when the variable equals itself
Symmetry property of congruence
If a=b then b=a
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…
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
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.
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
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…
38 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…
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
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…
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
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…
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
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.
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
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
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
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
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
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…
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
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
Honors Geometry Proofs and Postulates
Post 1: Ruler Postulate
Post 4
Post 5
Post 6
Once a coordinate system has been chosen in this way, the dis…
Angle Addition Post
a line contains at least 3 points not all in one line; a spac…
Through any two points there is exactly one line
Post 1: Ruler Postulate
Once a coordinate system has been chosen in this way, the dis…
Post 4
Angle Addition Post
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
38 terms
Geometry Chapter 2 postulates and proofs
Commutative
Associative
Identity
Inverse
Addition: a plus b equals b plus a... Mult: a times b equals b t…
Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…
Add: a plus 0 equals a... Mult: a times 1 equals a
Add: A plus negative a equals zero... Mult: a times 1/a equals 1
Commutative
Addition: a plus b equals b plus a... Mult: a times b equals b t…
Associative
Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…
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
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
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