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Study sets matching "chapter 1 geometry theorems"

20 terms
Geometry Chapter 1-Postulates, Definitions and Theorems
Ruler Postulate
Segment Addition Postulate
Congruent Figures
Congruent Segments
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
Have the same size and shape
Have equal lengths
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
10 terms
Geometry: Chapter 1 Theorems
Midpoint Theorem
Angle Bisector Theorem
Theorem 1-4
Theorem 1-5
if M is the midpoint of segment AB, then: 2AM=AB and AM=(1/2)…
if ray BX is the bisector of angle ABC, then: ... 2m angle ABX=m…
adjacent angles formed by perpendicular lines are congruent
if two lines form congruent adjacent angles, then the lines a…
Midpoint Theorem
if M is the midpoint of segment AB, then: 2AM=AB and AM=(1/2)…
Angle Bisector Theorem
if ray BX is the bisector of angle ABC, then: ... 2m angle ABX=m…
10 terms
Chapter 1 Geometry Theorems
right angle theorem
straight angle theorem
bisect/trisect theorem
congruent bisect/trisect theorem
If 2 angles are right angles, then they are congruent
If 2 angles are straight angles, then they are congruent
if a (point, segment, ray, or line) bisects/trisects a (segme…
if a (segment, angle) is divided into 2/3 congruent parts the…
right angle theorem
If 2 angles are right angles, then they are congruent
straight angle theorem
If 2 angles are straight angles, then they are congruent
9 terms
Geometry: Chapter 1 Postulates and Theorems
Expansion Postulate
Line Postulate
Plane Postulate
Flat Plane Postulate
A line contains at least two points. A plane contains at leas…
Any two points in space lie in exactly one line
Three distinct noncollinear points lie in exactly one plane
If two points lie in a plane, then the line containing these…
Expansion Postulate
A line contains at least two points. A plane contains at leas…
Line Postulate
Any two points in space lie in exactly one line
Geometry Theorems Chapter 1-5
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points of a line can be put into one-to-one correspondenc…
If three points A, B, and C are collinear and B is between A…
Consider ray OB and a point A on one side of ray OB. Every ra…
If point B is in the interior of Angle AOC, then the measurem…
Ruler Postulate
The points of a line can be put into one-to-one correspondenc…
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A…
Geometry: Postulates & Theorems (Chapter 1)
(Segment Addition Postulate) If B is b…
(Post. 5) A line contains at least _ p…
(Post. 6) Through any two points...
(Post. 7) Through any three noncolline…
AB + BC = AC
2, 3, 4
there is exactly one line
there is exactly one plane
(Segment Addition Postulate) If B is b…
AB + BC = AC
(Post. 5) A line contains at least _ p…
2, 3, 4
31 terms
Geometry - Chapter 1 - Foundations of Geometry - Theorems and Postulates
Postulate 1.1
Postulate 1.2
Postulate 1.3
Postulate 1.4
Given any TWO distinct POINTS in space, there is exactly ONE…
Given any THREE distinct POINTS in space NOT ON THE SAME LINE…
The line determined by any two distinct points in a plane is…
No plane contains all points in space.
Postulate 1.1
Given any TWO distinct POINTS in space, there is exactly ONE…
Postulate 1.2
Given any THREE distinct POINTS in space NOT ON THE SAME LINE…
11 terms
Geometry Chapter 1 Postulates and Theorems
If B is between A and C, then
If point D lies in the interior of ㄥAB…
If ㄥABC is a straight angle and D is a…
A line contains at least _____ points;…
AB + BC = AC
mㄥABD + mㄥCBD = mㄥABC
mㄥABD + mㄥCBD = 180॰
2, 3, 4
If B is between A and C, then
AB + BC = AC
If point D lies in the interior of ㄥAB…
mㄥABD + mㄥCBD = mㄥABC
Geometry chapter 1 theorems and definitions
If two angles are right angles
If two angles are straight angles
If a conditional statement is true
Lines
Then they are congruent
Then they are congruent
Then the contrapositive of the statement is true( if a, then…
They are made up of points with arrows at the end and are str…
If two angles are right angles
Then they are congruent
If two angles are straight angles
Then they are congruent
12 terms
Geometry Chapter 1-Postulates, Definitions and Theorems
Ruler Postulate
Segment Addition Postulate
Congruent Figures
Congruent Segments
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
Have the same size and shape
Have equal lengths
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
9 terms
Geometry Chapter 1 Postulates, Theorems, Formulas
Postulate
Ruler Postulate
Segment Addition Postulate
Midpoint Formula
Something we believe to be true but cannot prove.
The distance between two points is the absolute value of the…
If a point is between to other points then they MUST be colli…
M = {(x2+x1)/2 , (y2+y1)/2} or reverse {(x1+x2)/2 , (y1+y2)/2}
Postulate
Something we believe to be true but cannot prove.
Ruler Postulate
The distance between two points is the absolute value of the…
10 terms
Geometry Chapter 1 Postulates and Theorems
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 non-collinear 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…
38 terms
Theorems and Vocab for Geometry Chapter 1
points, lines and planes
line segment
ray
angle
undefined terms
a line with two endpoints;... set containing all points includin…
a line with one endpoint
union of two rays that share a common endpoint
points, lines and planes
undefined terms
line segment
a line with two endpoints;... set containing all points includin…
9 terms
Geometry: Postulates & Theorems (Chapter 1)
(Segment Addition Postulate) If B is b…
(Post. 5) A line contains at least _ p…
(Post. 6) Through any two points...
(Post. 7) Through any three noncolline…
AB + BC = AC
2, 3, 4
there is exactly one line
there is exactly one plane
(Segment Addition Postulate) If B is b…
AB + BC = AC
(Post. 5) A line contains at least _ p…
2, 3, 4
13 terms
Geometry Chapter 1 Postulates and Theorems
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
Geometry Chapter 1-Postulates, Definitions and Theorems
Ruler Postulate
Segment Addition Postulate
Congruent Figures
Congruent Segments
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
Have the same size and shape
Have equal lengths
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
10 terms
Geometry Chapter 1 Postulates and Theorems
Point-Line-Plane Postulate: a. Unique…
Point-Line-Plane Postulate: b. Number…
Point-Line-Plane Postulate: c. Dimensi…
Point-Line-Plane Postulate: c. Dimensi…
Through any two points there is exactly one line. If the two…
Every line is a set of points that can be put into a one-to-o…
There are at least two points in space.
Given a line in a plane, there is at least one point in the p…
Point-Line-Plane Postulate: a. Unique…
Through any two points there is exactly one line. If the two…
Point-Line-Plane Postulate: b. Number…
Every line is a set of points that can be put into a one-to-o…
9 terms
Geometry chapter 1 postulates and theorems
Expansion Postulate
Line postulate
Plane postulate
Flat plane postulate
A line contains at least two points... A plane contains at least…
Any two points in space lie in exactly one line
Three distinct noncollinear points lie in exactly one plane
If two points lie in a plane, then the line containing these…
Expansion Postulate
A line contains at least two points... A plane contains at least…
Line postulate
Any two points in space lie in exactly one line
8 terms
Geometry Postulates and Theorems Chapter 1.
Postulate 5
Postulate 6
Postulate 7
Postulate 8
The Dimension Postulate ... A line contains at least 2 points ... A…
Two points determine exactly one line
Any 3 points determine exactly one line (shows existence) ... 3…
If two points lie in a plane, the line that contains them lie…
Postulate 5
The Dimension Postulate ... A line contains at least 2 points ... A…
Postulate 6
Two points determine exactly one line
12 terms
Geometry Chapter 1- Postulates and Theorems
Postulate 1... Ruler Postulate
Postulate 2... Segment Addition Postulate
Postulate 3... Protractor Postulate
Postulate 4... Angle Addition Postulate
Ruler Postulate- ... Points on a line can be paired with real nu…
Segment Addition Postulate-... If B is between A and C, the AB +…
Protractor Postulate-... all rays of the interior of a straight…
Angle Addition Postulate-... If B lies on the interior of <AOC,…
Postulate 1... Ruler Postulate
Ruler Postulate- ... Points on a line can be paired with real nu…
Postulate 2... Segment Addition Postulate
Segment Addition Postulate-... If B is between A and C, the AB +…
9 terms
Chapter 1 Honors Geometry Theorems
Theorem 0
Theorem 1
Theorem (=~=) segs reflex
Theorem (=~=) segs sym
If 2 lines intersect, then they intersect at exactly one uniq…
A conditional is true if and only if it's contrapositive is t…
The congruence of segments is reflexive.
The congruence of segments is symmetric.
Theorem 0
If 2 lines intersect, then they intersect at exactly one uniq…
Theorem 1
A conditional is true if and only if it's contrapositive is t…
13 terms
Honors Geometry - Chapter 1 Postulates & Theorems
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactly one line.
If two lines intersect, then they intersect in exactly one po…
If two plains intersect, then they intersect in exactly one l…
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 lines intersect, then they intersect in exactly one po…
18 terms
Geometry Theorems Chapter 1-2
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
(How to measure with a ruler) Any line AB is equal in length…
If B is between A and C, then AB + BC = AC. If AB + BC = AC,…
(How to measure with a protactor) Any angle OAB is equal to t…
If P is in the interior of RST, then mRST=mRSP+mPST
Ruler Postulate
(How to measure with a ruler) Any line AB is equal in length…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC,…
9 terms
Geometry Chapter 1 Postulates and Theorems
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 exactly ___ ____.
Through any three noncollinear points there is exactly ___ __…
If two points lie in a plane, then the _________ containing t…
If two lines intersect, then they intersect in exactly ______…
Through any two points there is exactl…
Through any two points there is exactly ___ ____.
Through any three noncollinear points…
Through any three noncollinear points there is exactly ___ __…
64 terms
Geometry Postulates and Theorems Chapters 1-5
they are congruent.... Right Angles Cong…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Complem…
If two angles are right angles, then
If two angles are supplementary to the same angle, then
If two angles are supplementary to congruent angles, then
If two angles are complementary to the same angle, then
they are congruent.... Right Angles Cong…
If two angles are right angles, then
they are congruent.... Congruent Supplem…
If two angles are supplementary to the same angle, then
12 terms
Geometry Chapter 1 Postulates and Theorems
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate; The points on a line can be paired with the…
Segment Addition Postulate; If B is between A and C, then ... AB…
Protractor Postulate; We can measure angles with protractors.
Angle Addition Postulate; If point B lies in the interior of…
Postulate 1
Ruler Postulate; The points on a line can be paired with the…
Postulate 2
Segment Addition Postulate; If B is between A and C, then ... AB…
11 terms
Geometry Chapter 1 Theorems and Postulates
Angle Bisector Theorem
Line Postulate
Plane Postulate
Plane Intersection Postulate
If a ray is an angle bisector, then the sum of the two congru…
Through any two points there is exactly one line.
A plane contains at least three non-collinear points. Through…
If two planes intersect, they intersect in a line.
Angle Bisector Theorem
If a ray is an angle bisector, then the sum of the two congru…
Line Postulate
Through any two points there is exactly one line.
10 terms
Chapter 1 Geometry Theorems/Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
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=m<A…
Ruler Postulate
1. The points on a line can be paried with the real numbers i…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
24 terms
Geometry Definitions and Theorems Chapter 1
undefined term
point
line
plane
a term that cannot be defined by another figure (ex: points,…
names a location that has no size, represented by a dot and a…
a straight path that has no thickness, represented by a lower…
flat surface that has no thickness and extends forever, repre…
undefined term
a term that cannot be defined by another figure (ex: points,…
point
names a location that has no size, represented by a dot and a…
10 terms
Chapter 1 Geometry Theorems/Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
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=m<A…
Ruler Postulate
1. The points on a line can be paried with the real numbers i…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
12 terms
Geometry Chapter 1 Theorems and Postulates
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 3: Protractor Postulate
Postulate 4: 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
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=m<A…
Postulate 1: Ruler Postulate
the points on a line can be paired with the real numbers in s…
Postulate 2: Segment Addition Postulate
if B is between A and C, then AB+BC=AC
8 terms
Geometry Postulates and Theorems Chapter 1
Postulate 5
Postulate 6
Postulate 7
Postulate 8
A line contains at least two points; a plane contains at leas…
Through any two points, there is exactly one line.
Through any three points, there is at least one plane and thr…
If two points are in a plane, then the line that contains the…
Postulate 5
A line contains at least two points; a plane contains at leas…
Postulate 6
Through any two points, there is exactly one line.
14 terms
Geometry Chapter 1 Postulates And Theorems
Ruler Postulate
Segement Addition Postulate
Protractor Postulate
Angle Addition 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.
On a given plane, chose any point O between A and B. Consider…
If point B lies in the interior of angle AOC, then angle AOB…
Ruler Postulate
1. The points on a line can be paired with the real numbers i…
Segement Addition Postulate
If B is between A and C then AB +BC = AC.
24 terms
Geometry Chapter 1 & 2 Postulates/ Theorems
Definition of a Line
Definition of Intersecting Lines
Definition of Intersecting Planes
Definition of a Plane
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…
Definition of a Line
Through any two points there is exactly one line.
Definition of Intersecting Lines
If two distinct lines intersect, then they intersect in exact…
12 terms
Geometry Chapter 1: Postulates and Theorems
Ruler Postulate
Segment addition postulate
Protractor Postulate
Angle Addition Postulate
On a coordinate system, the absolute value of the difference…
If B is between A and C then AB + BC = AC
If ray OA = 0 and ray OB = 180, then the absolute value of th…
mLboc + mLaob = mLaoc. If the interior of angle AOC is angle…
Ruler Postulate
On a coordinate system, the absolute value of the difference…
Segment addition postulate
If B is between A and C then AB + BC = AC
10 terms
Geometry: Chapter 1 postulates and theorems
Postulate 5
Postulate 6
Postulate 7
Postulate 8
A line contains at least two points; a plane contains three p…
Through any two points, there is exactly one line
Through any three points, there is exactly one plane and thro…
If two points are in one plane, then the line that contains t…
Postulate 5
A line contains at least two points; a plane contains three p…
Postulate 6
Through any two points, there is exactly one line
25 terms
chapter 1 geometry theorems and definitions
net
isometric drawing
orthographic drawing
point
a 2 dimensional diagram that you can fold to form a a 3 dimen…
shows a corner view of a three dimensional figure ... (front and…
shows three separate views: a top view, a front view, and a r…
indicates a location and had no size
net
a 2 dimensional diagram that you can fold to form a a 3 dimen…
isometric drawing
shows a corner view of a three dimensional figure ... (front and…
Geometry Chapter 1 Postulates and Theorems
Segment Length Addition Postulate (SLAP)
Angle Measure Addition Postulate (AMAP)
A line contains at least...
A plane contains at least...
If B is between A and C, then AB + BC = AC.
If point B lies in the interior of ∠AOC, then m∠AOB+m∠BOC=180.
...2 points.
...3 points not all in one line.
Segment Length Addition Postulate (SLAP)
If B is between A and C, then AB + BC = AC.
Angle Measure Addition Postulate (AMAP)
If point B lies in the interior of ∠AOC, then m∠AOB+m∠BOC=180.
14 terms
HONORS GEOMETRY: Chapter 1 - Tool of Geometry Postulates, Theorems, and Constructions
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 in exactly on…
if two distinct planes intersect , then they intersect in exa…
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 intersect in exactly on…
12 terms
Geometry Chapter 1: Postulates and Theorems
Ruler Postulate
Segment addition postulate
Protractor Postulate
Angle Addition Postulate
On a coordinate system, the absolute value of the difference…
If B is between A and C then AB + BC = AC
If ray OA = 0 and ray OB = 180, then the absolute value of th…
mLboc + mLaob = mLaoc. If the interior of angle AOC is angle…
Ruler Postulate
On a coordinate system, the absolute value of the difference…
Segment addition postulate
If B is between A and C then AB + BC = AC
12 terms
Geometry Chapter 1 Postulates and Theorems
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 3
Postulate 4
The points on a line can be paired with the real numbers in s…
If B is in between A and C, then AB+BC=AC
How to set up and use a protractor
If point B lies in the interior of angle AOC, then the measur…
Postulate 1: Ruler Postulate
The points on a line can be paired with the real numbers in s…
Postulate 2: Segment Addition Postulate
If B is in between A and C, then AB+BC=AC
14 terms
Geometry Chapter 1 Postulates and Theorems
Postulate 1 ~ 1. (Ruler Postulate)
Postulate 1 ~ 2. (Ruler Postulate)
Postulate 2 (Segment Addition Postulate)
Postulate 4 ~ 1. (Angle Addition Postu…
The points on a line can be paired with the real numbers in s…
Once a coordinate system has been chosen in this way, the dis…
If B is between A and C, then AB+BC=AC.
If point B lies in the interior of angle AOC, then m of angle…
Postulate 1 ~ 1. (Ruler Postulate)
The points on a line can be paired with the real numbers in s…
Postulate 1 ~ 2. (Ruler Postulate)
Once a coordinate system has been chosen in this way, the dis…
Geometry Postulates and Theorems Chapter 1
Post 1
Post 2
Post 3
Post 4
ruler postulate
segment addition postulate
protractor postulate
angle addition postulate
Post 1
ruler postulate
Post 2
segment addition postulate
12 terms
Geometry Postulates and Theorems Chapter 1
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 3: Protractor Postulate
Postulate 4: Angle Addition 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
On AB in a given plane, choose any point O between A and B. C…
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 paired with the real numbers i…
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC
24 terms
Geometry Chapter 1-3 Theorems/Postulates
Point-line-plane Postulate
Line Intersection Theorem
Distance Postulate
Triangle Inequality Postulate
a.Unique line assumption... through any two points there is exac…
two different lines intersect in at most once
a. Uniqueness property On a coordinatized line, there is a un…
The sum of the lengths of any two sides of a triangle is grea…
Point-line-plane Postulate
a.Unique line assumption... through any two points there is exac…
Line Intersection Theorem
two different lines intersect in at most once
35 terms
Chapter 1-3 Geometry Postulates, Theorems, and Corollaries
true
false
true
false
Through any 2 points there is exactly one line (t or f)
Through any 2 points there isn't always a line (t or f)
Through any 3 noncollinear points there is exactly one plane…
Through any 4 noncollinear points there is exactly one plane…
true
Through any 2 points there is exactly one line (t or f)
false
Through any 2 points there isn't always a line (t or f)
10 terms
Geometry Chapter 1 Postulates, Theorems, and Corollaries
Through any two points there is exactl…
Through any three non collinear points…
If two points lie on a plane, then the…
If two lines intersect, then they inte…
...
...
...
...
Through any two points there is exactl…
...
Through any three non collinear points…
...
13 terms
Geometry Theorems Chapter 2
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Right Angle Congruence Theorem
Vertical angles are conguent.
If two angles are supplements of the same angle or a congruen…
If two angles are complements of the same angle, then the two…
All right angles are congruent
Vertical Angles Theorem
Vertical angles are conguent.
Congruent Supplements Theorem
If two angles are supplements of the same angle or a congruen…
34 terms
Geometry Terms/Theorems/Postulates CHAPTER 1
Inductive reasoning
Conjecture
Deductive reasoning
Point
reasoning based on patterns you observe
a concluding statement reached by using inductive reasoning
process of reasoning logically from given to a conclusion
a location in space
Inductive reasoning
reasoning based on patterns you observe
Conjecture
a concluding statement reached by using inductive reasoning
12 terms
Chapter 1 Geometry Postulates and Theorems - Chicko
ruler postulate (postulate one)
segment addition postulate (postulate…
protractor postulate (postulate three)
angle addition postulate (postulate fo…
the distance between two points equals the absolute value of…
If B is between A and C then:... AB + BC= AC
- on line AB in a given plane, choose any point O between A a…
- if point b lies in the interior of angle AOC, then:... m<AOB +…
ruler postulate (postulate one)
the distance between two points equals the absolute value of…
segment addition postulate (postulate…
If B is between A and C then:... AB + BC= AC
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