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Study sets matching "geometry postulates"

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Study sets matching "geometry postulates"

12 terms
Geometry- Postulates
segment addition postulate
angle addition postulate
a line contains at least two points
through any two points
If ABC then AB + AC = AC, ABC are collinear
If B is inside <AOC then m<AOB + m<BOC = m<AOC
a plane contains at least 3 noncollinear points, space contai…
there is exactly one line
segment addition postulate
If ABC then AB + AC = AC, ABC are collinear
angle addition postulate
If B is inside <AOC then m<AOB + m<BOC = m<AOC
18 terms
Geometry Postulates
Postulate 1: the ruler postulate
Postulate 2: the segment addition post…
Postulate 3
Postulate 4
The real number that corresponds to a point is the coordinate…
If B is between A & C, then AB + BC = AC. If AB + BC = AC, th…
Protractor Postulate
Angle Addition Postulate
Postulate 1: the ruler postulate
The real number that corresponds to a point is the coordinate…
Postulate 2: the segment addition post…
If B is between A & C, then AB + BC = AC. If AB + BC = AC, th…
9 terms
Geometry - Postulates
7
postulate
infinite
one
How many postulates are there?
a statement that is assumed true without proof
a line, plane, and space contain an _____________ number of p…
if there are two points, then exactly ______ line(s) contain(…
7
How many postulates are there?
postulate
a statement that is assumed true without proof
11 terms
Postulates-Geometry
Postulate
Postulate
Postulate
Segment Addition Postulate
Any two points are collinear
Any three non collinear points are coplanar
If two lines intersect they are coplanar
If L lies between D and Z, the DL+LZ=DZ
Postulate
Any two points are collinear
Postulate
Any three non collinear points are coplanar
10 terms
Geometry postulates
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 noncollinear points there is exactly one pl…
1-1
Through any two points there is exactly one line
1-2
If two distinct lines intersect, then they intersect in exact…
14 terms
Geometry Postulates
Postulate 1: Ruler Postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
Given any 2 points, exactly one straight line can be drawn th…
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 P is in the interior of <RST, then m<RSP + m<PST = m<RST
Postulate 1: Ruler Postulate
Given any 2 points, exactly one straight line can be drawn th…
Segment addition postulate
If B is between A and C then AB+BC=AC
13 terms
Geometry postulates
Angle addition postulate
ASA Congruence Postulate
Right Angles are congruent Theorem
Converse of the interior supplements t…
If point D lies in the interior of <ABC, then m<ABD + m<DBC =…
If two angles and the included side and the included side in…
Al right angles are congruent
If two lines are cut by a transversal forming interior angles…
Angle addition postulate
If point D lies in the interior of <ABC, then m<ABD + m<DBC =…
ASA Congruence Postulate
If two angles and the included side and the included side in…
16 terms
Geometry Postulates
Three
Two
Line
One Line
A plane contains at least _____________ points, not on the sa…
A line contains at least ______________ points.
If two planes intersect, then their intersection is a _______…
Through any two points there is exactly __________ __________…
Three
A plane contains at least _____________ points, not on the sa…
Two
A line contains at least ______________ points.
14 terms
Geometry postulates
Addition POE
Subtraction POE
Multiplication POE
Division POE
if A=B then A+C = B+C
if A=B then A-C = B-C
If A=B then AxC = BxC
If A=B then A/C = B/C
Addition POE
if A=B then A+C = B+C
Subtraction POE
if A=B then A-C = B-C
11 terms
Geometry Postulates
1 Ruler Postulate
2 Segment Addition Postulate
3 Protractor Postulate
4 Angle Addition Postulate
-the distance between two points is absolute value of the dif…
-if B is between A and C, then AB+BC=AC
-the measure of an angle is the absolute value of the differe…
-if point P is the interior of angle:ABC, then the measure of…
1 Ruler Postulate
-the distance between two points is absolute value of the dif…
2 Segment Addition Postulate
-if B is between A and C, then AB+BC=AC
20 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on any line can be paired with real numbers such t…
If Q is between P and R, then PQ+QR=PR.
Given ray AB and a number, R, that's between 0 and 180, there…
If point R is in the interior of angle PQS, then the measure…
Ruler Postulate
The points on any line can be paired with real numbers such t…
Segment Addition Postulate
If Q is between P and R, then PQ+QR=PR.
9 terms
Geometry - 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 have exactly one point.
If two distinct planes intersect, they have exactly one line.
Through any three noncollinear points there is exactly one pl…
Postulate 1-1
Through any two points there is exactly one line.
Postulate 1-2
If two distinct lines intersect, they have exactly one point.
9 terms
Geometry postulates
postulate 1-2
postulate 1-3
postulate 1-1
postulate 1-4
if two distinct lines intersect, then they intersect at exact…
if two distinct planes intersect, then they intersect in exac…
through any two points there is exactly one line
through any 3 noncollinear points there is exactly one plane
postulate 1-2
if two distinct lines intersect, then they intersect at exact…
postulate 1-3
if two distinct planes intersect, then they intersect in exac…
9 terms
Geometry Postulates
Postulates 1-1
Postulates 1-2
Postulates 1-3
Postulates 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 noncollinear points there is exactly one pl…
Postulates 1-1
Through any two points there is exactly one line
Postulates 1-2
If two distinct lines intersect, then they intersect in exact…
10 terms
Geometry-Postulates-The Basics
Through any two points there is exactl…
Through any three noncollinear points…
If two points lie in a plane, then the…
If two lines intersect, then they inte…
Through any two points there is exactl…
Through any three noncollinear points…
8 terms
Geometry 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, then they intersect in exact…
if two distinct planes intersect, then they intersect in exac…
through any three noncollinear points there is exactly one pl…
Postulate 1-1
through any two points there is exactly one line.
Postulate 1-2
if two distinct lines intersect, then they intersect in exact…
14 terms
Geometry Postulates
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Perpendicular to Parallel Theorem
If two parallel lines are cut by a transversal, then the corr…
If two parallel lines are cut by a transversal, then the alte…
If two parallel lines are cut by a transversal, then the alte…
If two lines in the same plane are perpendicular to a third l…
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the corr…
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the alte…
9 terms
geometry postulates
postulate 1-1
postulate 1-2
postulate 1-3
postulate 1-4
Through any two points, there is exactly 1 line.
If 2 distinct lines intersect, then they intersect at exactly…
If two distint planes intersect then they intersect at exactl…
Through any three noncollinear points there is exactly one pl…
postulate 1-1
Through any two points, there is exactly 1 line.
postulate 1-2
If 2 distinct lines intersect, then they intersect at exactly…
12 terms
Geometry postulates
Postulate 1
Segment addition postulate
Protractor Postulate
Angle Addition postulate
What can be paired with real numbers to etablish coordinate s…
AB+BC=AC
This is similar to the ruler postulate; if you have a pair of…
If point B lies in the interior of <AOC then m<AOB + m<BOC =…
Postulate 1
What can be paired with real numbers to etablish coordinate s…
Segment addition postulate
AB+BC=AC
19 terms
Geometry Postulates
Postulate 1 (Ruler Postulate)
Postulate 2 (Segment Addition Postulate)
Postulate 3 (Protractor Postulate)
Postulate 4 (Angle Addition Postulate)
The distance between points A and B (AB) is the absolute valu…
If B is between A and C then AB+BC=AC
The measure of <AOB is equal to the absolute value of the dif…
If ray P is in the center of <RST then the m<RSP+m<PST=m<RST
Postulate 1 (Ruler Postulate)
The distance between points A and B (AB) is the absolute valu…
Postulate 2 (Segment Addition Postulate)
If B is between A and C then AB+BC=AC
23 terms
Geometry Postulates
Postulate
Ruler postulate
Segment addition postulate
Protractor postulate
A statement that is accepted as true without proof
The points on a line can be matched one to one with the real…
If B is between A and C, then AB 1 BC 5 AC. If AB 1 BC 5 AC,…
Consider Ray OB and a point A on one side of Ray OB . The ray…
Postulate
A statement that is accepted as true without proof
Ruler postulate
The points on a line can be matched one to one with the real…
16 terms
Geometry Postulates
a=a
If a=b and b=c, then a=c
If a=b, then b=a
If a=b, then a+c = b+c
Reflexive property
Transitive property
Symmetric property
Addition property
a=a
Reflexive property
If a=b and b=c, then a=c
Transitive property
9 terms
Geometry: Postulates
Postulate 1 (Ruler Postulate)
Postule 2 (Segment Addition Postulate)
Postulate 3 (Protractor Postulate)
Postulate 4 (Angle Addition Postulate)
1. The points on a line can be paried with the real numbers i…
If B is between A and C, then AB + BC = AC.
On Line AB in a given plane, choose any point O between A and…
If Point B lies in the interior of <AOC, then m<AOB + m<BOC =…
Postulate 1 (Ruler Postulate)
1. The points on a line can be paried with the real numbers i…
Postule 2 (Segment Addition Postulate)
If B is between A and C, then AB + BC = AC.
27 terms
Geometry Postulates
Postulate 1-1-1
Postulate 1-1-2
Postulate 1-1-3
Postulate 1-1-4
Through any two points there is exactly one line.
Through any three non collinear points there is exactly one p…
If two points lie in a plane, then the line containing those…
If two lines intersect, then they intersect at exactly one po…
Postulate 1-1-1
Through any two points there is exactly one line.
Postulate 1-1-2
Through any three non collinear points there is exactly one p…
9 terms
Geometry Postulates
Law of Syllogism
Law of Detachment
Postulate 5
Postulate 6
If hypothesis p, then conclusion q.... If hypothesis q, then con…
If the hypothesis of a true statement is true, then ... the conc…
Through any two points there exists exactly one line.
A line contains at least two points.
Law of Syllogism
If hypothesis p, then conclusion q.... If hypothesis q, then con…
Law of Detachment
If the hypothesis of a true statement is true, then ... the conc…
9 terms
Geometry 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, then they intersect in exact…
If two distinct planes intersect then they intersect in exact…
Through any three noncollinear points there is exactly one pl…
Postulate 1-1
Through any two points there is exactly one line.
Postulate 1-2
If two distinct lines intersect, then they intersect in exact…
9 terms
Geometry Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two parts there is exactly one line
If two distinct lines intersect, then they intersect at exact…
If two distinct planes intersect, then they intersect at exac…
Through any three noncollinear points there is exactly one pl…
Postulate 1-1
Through any two parts there is exactly one line
Postulate 1-2
If two distinct lines intersect, then they intersect at exact…
9 terms
Geometry 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, then they intersect in exact…
If two distinct planes intersect, then they intersect in exac…
Through any three nonconllinear points there is exactly one p…
Postulate 1-1
Through any two points there is exactly one line.
Postulate 1-2
If two distinct lines intersect, then they intersect in exact…
10 terms
geometry postulates
through any ____ points there is exact…
through any three ________ points, the…
a line contains at least __ points.
a plane contains at least ___ noncolli…
two, line
noncollinear, plane
2
3
through any ____ points there is exact…
two, line
through any three ________ points, the…
noncollinear, plane
11 terms
Postulates for Geometry
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Postulate 1
Ruler Postulate
Postulate 2
Segment Addition Postulate
12 terms
geometry: postulates
corresponding angles postulate
alternate interior angles theorem
alternate exterior angles theorem
consecutive interior angles theorem
if 2 parallel limes are cut by a transversal, then EACH PAIR…
if 2 parallel lines are cut by a transversal, then EACH PAIR…
If 2 parallel lines are cut by a transversal, then EACH PAIR…
If 2 parallel lines are cut by a transversal, then EACH PAIR…
corresponding angles postulate
if 2 parallel limes are cut by a transversal, then EACH PAIR…
alternate interior angles theorem
if 2 parallel lines are cut by a transversal, then EACH PAIR…
12 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Angle Addition Postulate
Protractor Postulate
1. The points on a line can be paired with the real numbers i…
If B is between A and C, then AB+BC=AC
If point B lies in the interior of angle AOC, then the measur…
On line AB in a given plane, choose any point 0 between A and…
Ruler Postulate
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
16 terms
Geometry Postulates
If B is between A and C... (segment addit…
If B lies interior of <AOC... (angle addi…
Through any 2 points
Through any 3 noncollinear points
then AB+BC=AC
m<AOB+m<BOC=m<AOC
there is exactly 1 line
there is exactly 1 plane
If B is between A and C... (segment addit…
then AB+BC=AC
If B lies interior of <AOC... (angle addi…
m<AOB+m<BOC=m<AOC
19 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Linear Pair Postulate
Parallel Postulate
The points on a line can be matched one to one with the real…
What postulate does this rule reflect?... If B is between A and…
If two angles form a linear pair, then they are supplementary.
If there is a line and a point not on the line, then there is…
Ruler Postulate
The points on a line can be matched one to one with the real…
Segment Addition Postulate
What postulate does this rule reflect?... If B is between A and…
14 terms
Postulates in Geometry
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Postulate 1
Ruler Postulate
Postulate 2
Segment Addition Postulate
7 terms
Postulates in Geometry
Angle Addition Postulate
Segment Addition Postulate
Linear Pair Postulate
Parallel Postulate
If point B lies in the interior of ∠AOC then m∠AOB+m∠BOC=m∠AOC
If three points A, B, and C are collinear and B is between A…
If two angles form a linear pair, then they are supplementary
If there is a line and a point not on the line, then there is…
Angle Addition Postulate
If point B lies in the interior of ∠AOC then m∠AOB+m∠BOC=m∠AOC
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A…
11 terms
Postulates in Geometry
There is one line that runs through po…
Line CD contains at least points C and D
Point M is at the intersection between…
Noncollinear points F, G, and H form p…
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…
There is one line that runs through po…
Through any two points there exists exactly one line.
Line CD contains at least points C and D
A line contains at least two points.
6 terms
Geometry Postulates & Theorems
Corresponding Angles Converse
Alternate Interior Angles Converse
Alternative Exterior Angles Converse
Consecutive Interior Angles converse
If two lines are cut by a transversal so the corresponding an…
If two lines are cut by a transversal so the alternate interi…
if two lines are cut by a transversal so the alternate exteri…
If two lines are cut by a transversal so the consecutive inte…
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding an…
Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interi…
19 terms
Geometry Honors Theorems & Postulates
Right Angle Congruence Theorem
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
If 2 angles are right angles, then they are congruent
If 2 angles are vertical angles, then they are congruent
If 2 angles are supplementary to the same angle or congruent…
If 2 angles are complementary to the same angle or congruent…
Right Angle Congruence Theorem
If 2 angles are right angles, then they are congruent
Vertical Angles Theorem
If 2 angles are vertical angles, then they are congruent
11 terms
Geometry Postulates
through any two points there is exactl…
if two distinct lines intersect, then…
if two planes intersect, then they int…
through any three non collinear points…
line
point
line
plane
through any two points there is exactl…
line
if two distinct lines intersect, then…
point
13 terms
geometry postulates and theroms
points existence postulate
straight line postulate
plane postulate
flat plane postulate
space contains at least four noncoplanar points. every plane…
two points are contained in one and only one line (two points…
three noncollinear points are contained in one and only one p…
if two points are in a plane, then the line containing the po…
points existence postulate
space contains at least four noncoplanar points. every plane…
straight line postulate
two points are contained in one and only one line (two points…
74 terms
Geometry Definitions, Postulates and Theorems
Complementary angles
Supplementary angles
Theorem
Vertical Angles
two angles whose measures have a sum of 90°
two angles who measures have a sum of 180°
a statement that can be proven
two angles formed by intersecting lines and facing in the opp…
Complementary angles
two angles whose measures have a sum of 90°
Supplementary angles
two angles who measures have a sum of 180°
11 terms
Postulates for Geometry
postulate or axiom
Postulate 1.1
Postulate 1.2
Postulate 1.3
an accepted statement of fact
Through any two points, there is exactly one line
If 2 lines intersect, they intersect at exactly one point
If 2 planes intersect, they intersect at exactly one line
postulate or axiom
an accepted statement of fact
Postulate 1.1
Through any two points, there is exactly one line
25 terms
Postulates for Geometry
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Only one straight line can be drawn through two points; two p…
A straight line is the shortest line connecting two points in…
A line segment can be bisected at only one point.
Two lines in the same plane either intersect or are parallel.…
Postulate 1
Only one straight line can be drawn through two points; two p…
Postulate 2
A straight line is the shortest line connecting two points in…
16 terms
Important Geometry Theorems/Postulates
If two congruent angles form a linear…
If two angles are vertical angles, the…
If there is a line and a point not on…
If there exists a line and a point, th…
If two congruent angles form a linear…
If two angles are vertical angles, the…
39 terms
Geometry Theorems, Postulates, & Definitions
Segment Addition Postulate
Angle Addition Postulate
Definition of Midpoint & Bisector
Definition of Angle Bisector
If B is between A and C then the length of AC is equal to the…
If P is in the interior of ∠RST then the measure of ∠RST is t…
A bisector bisects a line segment at its midpoint which divid…
A ray that divides an angle into two adjacent angles that are…
Segment Addition Postulate
If B is between A and C then the length of AC is equal to the…
Angle Addition Postulate
If P is in the interior of ∠RST then the measure of ∠RST is t…
23 terms
GEOMETRY-POSTULATE
RULER POSTULATE
SEGMENT ADDITION POSTULATE
PROTRACTOR POSTULATE
ANGLE ADDITION POSTULATE
The points on a line can be paired with the real numbers in s…
If B is between A and C, then AB + BC = AC
Consider RayOB and a point A on one side of RayOB. The rays o…
DAGAS, If B is in the interior of angle AOC, then the measure…
RULER POSTULATE
The points on a line can be paired with the real numbers in s…
SEGMENT ADDITION POSTULATE
If B is between A and C, then AB + BC = AC
12 terms
Geometry - Postulates and theorems
segment addition postulate
reflexive property
congruent
midpoint theorem
AB + BC = AC
any segment or angle is congruent/equal to itself (AB = AB) (…
have equal measure
If AB + BC = AC and AB=BC
segment addition postulate
AB + BC = AC
reflexive property
any segment or angle is congruent/equal to itself (AB = AB) (…
11 terms
GEOMETRY POSTULATES
Postulate 1... Ruler postulate
Postulate 2... Segment addition postulate
Postulate 3... Protractor postulate
Postulate 4... Angle addition postulate
The points on one line can be matched exactly to real numbers…
If B is between A and C, than AB + BC = AC
We haven't learned it yet
If you place two angles side-by-side then the measure of the…
Postulate 1... Ruler postulate
The points on one line can be matched exactly to real numbers…
Postulate 2... Segment addition postulate
If B is between A and C, than AB + BC = AC
6 terms
Geometry postulates
Addition postulate
Subtraction postulate
Reflexive postulate
Partition postulate
If equal quantities are added to equal quantities, the sums a…
If equal quantities are subtracted from equal quantities, the…
A quantity is congruent (equal) to itself.
The whole is equal to the sum of its parts
Addition postulate
If equal quantities are added to equal quantities, the sums a…
Subtraction postulate
If equal quantities are subtracted from equal quantities, the…
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