Study sets matching "geometry postulates"

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Study sets matching "geometry postulates"

22 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
15 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
5 terms
Geometry Postulates
Postulate 1
Postulate 2
The Ruler Postulate (Postulate 3)
The Protractor Postulate (Postulate 4)
Two points determine a unique straight line.
Three noncollinear points determine a unique plane
a. To every point on a line there corresponds exactly one rea…
a. The rays in a half rotation (180 degrees) can be numbered…
Postulate 1
Two points determine a unique straight line.
Postulate 2
Three noncollinear points determine a unique plane
9 terms
Geometry: Postulates
Postulate 1.2
Postulate 1.3-1 (Two Points Determine…
Postulate 1.3-2 (Intersection of Lines)
Postulate 1.3-3 (Intersection of Planes)
Two points make a line
Two lines intersect at a point
Two planes intersect at a line
Two planes intersect at a line
Postulate 1.2
Two points make a line
Postulate 1.3-1 (Two Points Determine…
Two lines intersect at a point
11 terms
Geometry Postulates
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,…
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 lines intersect, then they intersect in exactly one po…
If two planes 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…
8 terms
Geometry Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Through any two points there is exactly one line
If two lines intersect they intersect in exactly one point
If two planes intersect, they intersect in exactly one line
Through any three non-collinear points there exists exactly o…
Postulate 1
Through any two points there is exactly one line
Postulate 2
If two lines intersect they intersect in exactly one point
Geometry - Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
accepted rule that a ruler can find a distance
if B is between A and C, then AB + BC = AC
the measure of an angle is equal to the absolute value of the…
if P is in the interior of the angle RST, then the measure of…
Ruler Postulate
accepted rule that a ruler can find a distance
Segment Addition Postulate
if B is between A and C, then AB + BC = AC
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Given two points, there corresponds a unique positive number…
Given two rays, there corresponds a unique positive number ca…
Ruler Postulate
Given two points, there corresponds a unique positive number…
Segment Addition Postulate
geometry postulates
Postulate 1- Ruler Postulate
Postulate 2- Segment Addition Postulate
Postulate 3
Postulate 4- Angle Addition Postulate
the points on a line can be paired with the real numbers in s…
ex. if B is between A and C then: AB+BC=AC
rays can be paired with the real numbers from 1-180
if a point lies in the interior of and angle, then you would…
Postulate 1- Ruler Postulate
the points on a line can be paired with the real numbers in s…
Postulate 2- Segment Addition Postulate
ex. if B is between A and C then: AB+BC=AC
22 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
8 terms
Geometry Postulates
Postulate(a statement that is accepted…
Postulate 2
Postulate 3, postulate 4
Postulate 5
The points on a line can be paired in a one-to-one correspond…
If B is between A and C, then AB+BC=AC
Please see the text book for diagram explanation
Through any two points there is exactly one line
Postulate(a statement that is accepted…
The points on a line can be paired in a one-to-one correspond…
Postulate 2
If B is between A and C, then AB+BC=AC
18 terms
Geometry 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 matched one to one with the real…
If B is between A and C, then AB + BC = AC ... AND ... If AB + BC =…
<AOB is equal to the absolute value of the difference between…
If B is the interior of angle AOC, then the measure of angle…
Postulate 1 - Ruler Postulate
The points on a line can be matched one to one with the real…
Postulate 2 - Segment Addition Postulate
If B is between A and C, then AB + BC = AC ... AND ... If AB + BC =…
11 terms
Geometry Postulates
ruler postulate
segment addition postulate
protractor postulate
angle addition postulate
the points on a line can paired in a one-to-one correspondenc…
if B is between A and C, then AB + BC = AC
given a point X on line PR, consider rays XP and XR as well a…
if point D is in the interior of angle ABC, then m angleABD +…
ruler postulate
the points on a line can paired in a one-to-one correspondenc…
segment addition postulate
if B is between A and C, then AB + BC = AC
18 terms
Geometry Postulates
The Distance Postulate (2-4)
The Ruler Postulate (2-5)
The Ruler Placement Postulate (2-5)
The Line Postulate
To every pair of different points there corresponds a unique…
1. One point of the line for each number... 2. One number for ea…
Given 2 Points of a line, the coordinate system can be shifte…
For every two different points there is exactly one line that…
The Distance Postulate (2-4)
To every pair of different points there corresponds a unique…
The Ruler Postulate (2-5)
1. One point of the line for each number... 2. One number for ea…
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
14 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
10 terms
Geometry Postulates Chapter 1
Postulate 1-1 Through any two points,…
Postulate 1-2 If two distinct lines in…
Postulate 1-3 If two distinct _______i…
Postulate 1-4 Through any ________poin…
line
point
planes
three noncollinear
Postulate 1-1 Through any two points,…
line
Postulate 1-2 If two distinct lines in…
point
14 terms
Geometry: Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
If you take a line segment and divide it into equal segments…
If B is between A and C, then AB + BC = AC (the parts add up…
On line AB in a given plane, chose any point O between A and…
If point B lies in the interior of /_AOC, then the m/_AOB + m…
Ruler Postulate
If you take a line segment and divide it into equal segments…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC (the parts add up…
Geometry Postulates
Side Angle Side (SAS)
Side Side Side (SSS)
Included Angles
Included Sides
If 2 sides and an included angle are congruent to 2 sides and…
Three sides of one triangle are congruent to three sides of t…
Angle formed by 2 adjacent sides
Sides located between 2 angles
Side Angle Side (SAS)
If 2 sides and an included angle are congruent to 2 sides and…
Side Side Side (SSS)
Three sides of one triangle are congruent to three sides of t…
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The distance between points A and B, written as AB, is the ab…
If B is between A and C, then AB+ BC= AC
The measure of angle AOB is equal to the absolute value of th…
If P is the interior of angle RST, then the measure of angle…
Ruler Postulate
The distance between points A and B, written as AB, is the ab…
Segment Addition Postulate
If B is between A and C, then AB+ BC= AC
Geometry Lines Postulates
collinear points
coplanar
parallel lines
parallel planes
Points that lie on the same line.
points that lie on the same plane
coplanar lines that do not intersect
planes that do not intersect.
collinear points
Points that lie on the same line.
coplanar
points that lie on the same plane
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…
19 terms
Geometry Postulates
Transitive Postulate
Substitution Postulate
Partition Postulate
Reflexive Postulate
Equal things are equal.... If A=B and C=B, then A=C
A quantity may be substituted for its equal in any expression…
The whole equals the sum of its parts.
Any quantity equals itself.
Transitive Postulate
Equal things are equal.... If A=B and C=B, then A=C
Substitution Postulate
A quantity may be substituted for its equal in any expression…
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°
Geometry postulates
ruler postulate
Segment Addition Postulate (Seg. Add.…
Protractor Postulate
Angle Addition Postulate
1.)points must be put on a number line... 2.)the distance betwee…
if B is between A and C, then AB+BC=AC (page 12 in book)
used to find the measure of an angle... 1.) take the absolute va…
m<AOB + m<BOC = m< AOC
ruler postulate
1.)points must be put on a number line... 2.)the distance betwee…
Segment Addition Postulate (Seg. Add.…
if B is between A and C, then AB+BC=AC (page 12 in book)
Geometry Postulates
Postulate 1
Postulate 2
Postulate 3 The Ruler Postulate
Postulate 4 The Protractor Postulate
Two points determine a line.
Three noncollinear points determine a line.
The points on a line can be numbered so that positive number…
The rays in a half-rotation can be numbered from 0 to 180 so…
Postulate 1
Two points determine a line.
Postulate 2
Three noncollinear points determine a line.
Geometry-Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be match one to one with real number…
If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B i…
Consider a point A on one side of line OB. The rays of a form…
If P is in the interior of ∠RST, then m∠RSP+m∠PST=m∠RST.
Ruler Postulate
The points on a line can be match one to one with real number…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B i…
14 terms
Geometry Postulates and Theorums
Same Side Interior Angles Postulate
Alternate Interior Angles Theorem
Corresponding Angles Theorem
Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then the same…
If a transversal intersects two parallel lines, then alternat…
If a transversal intersects two parallel lines, then correspo…
If a transversal intersects two parallel lines, then alternat…
Same Side Interior Angles Postulate
If a transversal intersects two parallel lines, then the same…
Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternat…
Geometry Postulates
Postulate 5
Postulate 6
Postulate 7
Postulate 8
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…
Postulate 5
Through any two points there exists exactly one line.
Postulate 6
A line contains at least two points.
10 terms
Geometry Postulates
Through any two points, there exists e…
A line contains at least two points.
If two lines intersect, their intersec…
Through any three nocollinear points t…
Through any two points, there exists e…
A line contains at least two points.
14 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
15 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate (SAP)
Protractor Postulate
Angle Addition Postulate (AAP)
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
1. OA is paired with 0, and OB with 180... 2. If OP is paired wi…
If point B lies in the interior of <AOC , then m<AOB + m<BOC…
Ruler Postulate
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate (SAP)
If B is between A and C, then AB+BC=AC
Geometry postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
"The ruler postulate" measure the distance between any two po…
"Segment Addition postulate" you can add two adjacent (right…
"Protractor postulate" two places where the angle intersects…
"Angle addition postulate" you can add two adjacent (right ne…
Postulate 1
"The ruler postulate" measure the distance between any two po…
Postulate 2
"Segment Addition postulate" you can add two adjacent (right…
Geometry Postulates
Postulate
Purpose of a Postulate
Unique-Line-Assumption
Three Ways to Name Unique Lines
Assumptions, a statement assumed to be true, also called an A…
To explain undefined terms. To serve as a starting point for…
Through any two points there is ONE line
1) cursive l ... 2) AB... 3) BA
Postulate
Assumptions, a statement assumed to be true, also called an A…
Purpose of a Postulate
To explain undefined terms. To serve as a starting point for…
8 terms
Geometry Postulates
Two Point Postulate
Line intersection postulate
Three point postulate
Plane line postulate
Through any two points there exists exactly one line
If two lines intersect then there intersection is exactly 1 p…
Through any three noncollinear points there exists exactly 1…
If two points lie in a plane then the line containing them li…
Two Point Postulate
Through any two points there exists exactly one line
Line intersection postulate
If two lines intersect then there intersection is exactly 1 p…
10 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 lines intersect, then they intersect in exactly one po…
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 lines intersect, then they intersect in exactly one po…
12 terms
Geometry: Postulates
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 pl…
any line contains at least two points
any 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 pl…
Geometry Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any 2 points there is exactly one line.
If 2 distinct lines intersect, then they intersect in exactly…
If two distinct planes intersect, they intersect in exactly o…
Through any non-collinear points there is exactly one plane.
Postulate 1-1
Through any 2 points there is exactly one line.
Postulate 1-2
If 2 distinct lines intersect, then they intersect in exactly…
19 terms
Postulates - Geometry
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 line AB in a given plane, choose any point O between A and…
If point B lies in the interior of angle AOC, then measure of…
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
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 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…
15 terms
Geometry Postulates
Isometry
Transformation
Rigid Motion
Pre-image
A transformation that is rigid
A change in position, size, or shape of a geometric figure
Transformations that preserve distance and angle measure.
The original picture
Isometry
A transformation that is rigid
Transformation
A change in position, size, or shape of a geometric figure
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 lines intersect, then they intersect in exactly one po…
If two planes 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…
Geometry Postulates
Through any 2 points there is exactly…
Through any 3 points NOT on the same l…
A line contains at least 2...
A plane contains at least 3 points...
Line
There is exactly one plane
Points
Not on the same line
Through any 2 points there is exactly…
Line
Through any 3 points NOT on the same l…
There is exactly one plane
9 terms
Geometry- Postulates
1
2
3
4
Through any two points there is exactly one line
If two distinct lines intersect, then they intersect at exact…
If two distinct planes intersect, then they intersect in exac…
Through any three non collinear points there is exactly one p…
1
Through any two points there is exactly one line
2
If two distinct lines intersect, then they intersect at exact…
Geometry Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate: Points on a line that match the real numbers…
Segment Addition Postulate: If B is between A and C, then AB…
Protractor Postulate: We can number and measure angles.
Angle Addition Postulate: If two angles share a vertex, you c…
Postulate 1
Ruler Postulate: Points on a line that match the real numbers…
Postulate 2
Segment Addition Postulate: If B is between A and C, then AB…
13 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
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.
10 terms
Geometry Postulates
segment addition postulate
angle addition postulate
postulate
postulates 1
If B is between A and C then AB+BC=AC
If point B lies in the interior of angle AOC then the measure…
a basic assumption
a line contains at least two points; a plane contains at leas…
segment addition postulate
If B is between A and C then AB+BC=AC
angle addition postulate
If point B lies in the interior of angle AOC then the measure…
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
1 of 10