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Study sets matching "postulates"

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Study sets matching "postulates"

48 terms
Postulates
Intersection of lines
Intersection of planes
Three non collinear points determine a…
Ruler Postulate
If two distinct lines intersect, they intersect at exactly on…
If two distinct planes intersect, then they intersect in exac…
Through any three non collinear points, there is exactly one…
Every point of a line can be placed in correspondence with a…
Intersection of lines
If two distinct lines intersect, they intersect at exactly on…
Intersection of planes
If two distinct planes intersect, then they intersect in exac…
14 terms
Postulates
1.1 Ruler Postulate
1.2 Segment Addition Postulate
1.3 Protractor Postulate
1.4 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.... If AB + BC =AC, t…
Consider line OB and a point A on one side of line OB. The ra…
If P is in the interior of andgle RST, then the measure of an…
1.1 Ruler Postulate
The points on a line can be matched one to one with the real…
1.2 Segment Addition Postulate
If B is between A and C, then AB + BC = AC.... If AB + BC =AC, t…
9 terms
Postulates
through any two points
through any three noncollinear points
on any line
on any plane
there is exactly one line
there is exactly one plane
there are at least two points
there are at least 3 noncollinear points
through any two points
there is exactly one line
through any three noncollinear points
there is exactly one plane
14 terms
Postulates
Ruler Postulate (Postulate 1)
Segment Addition Postulate (Postulate 2)
Protractor Postulate (Postulate 3)
Angle Addition Postulate (Postulate 4)
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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.
Ruler Postulate (Postulate 1)
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate (Postulate 2)
If B is between A and C, then AB+BC=AC.
19 terms
POSTULATES
AB + BC = AC (part + part = whole)
m∠ABC = m∠ABP + m∠CBP ... (part + part =…
exactly 1 line.
2 points.
P2 - The Segment Addition Postulate... If B is between points A…
P4 - The Angle Addition Postulate... If P is a point interior to…
P5... Through any two points there exists
P6... A line contains at least
AB + BC = AC (part + part = whole)
P2 - The Segment Addition Postulate... If B is between points A…
m∠ABC = m∠ABP + m∠CBP ... (part + part =…
P4 - The Angle Addition Postulate... If P is a point interior to…
10 terms
Postulates
Ruler Postulate
Protractor Postulate
Linear Pair Postulate
Segment Addition Postulate
...
...
...
Ruler Postulate
Protractor Postulate
...
10 terms
POSTULATES
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
through any two given points there is one line
If two distinct lines intersect, they intersect in exactly on…
If two distinct planes intersect, they intersect in exactly o…
Through any three noncollinear points there is exactly one pl…
Postulate 1-1
through any two given points there is one line
Postulate 1-2
If two distinct lines intersect, they intersect in exactly on…
11 terms
Postulates
Postulate #1
Postulate #2
Postulate #3
Postulate #4
RULER POSTULATE - On a number line, every point can be paired…
SEGMENT ADDITION POSTULATE -
PROTRACTOR POSTULATE -
ANGLE ADDITION POSTULATE -
Postulate #1
RULER POSTULATE - On a number line, every point can be paired…
Postulate #2
SEGMENT ADDITION POSTULATE -
9 terms
Postulates
Postulate 1
Postulate 2
The Ruler Postulate
Corollary to Ruler Postulate
Two points determine a line
Three noncollinear points determine a plane
The points on a line can be numbered so that positive number…
A line segment has exactly ONE midpoint
Postulate 1
Two points determine a line
Postulate 2
Three noncollinear points determine a plane
9 terms
Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Two points on a line can be paired with real numbers... (A=0,B=1…
AB+BC=AC
You can pair rays with real #s... (if OP=x and OQ=y then m<POQ=I…
exactly like segment addition postulate
Ruler Postulate
Two points on a line can be paired with real numbers... (A=0,B=1…
Segment Addition Postulate
AB+BC=AC
6 terms
Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Two points determine a unique straight line.
Three noncollinear points determine a unique plane.
The Ruler Postulate: (a) To every point on a line, there corr…
The Protractor Postulate: (a) The rays in a half rotation (18…
Postulate 1
Two points determine a unique straight line.
Postulate 2
Three noncollinear points determine a unique plane.
16 terms
Postulates
two point postulate/line point postulate
line intersection postulate
three point postulate
plane point postulate
through any two points there exists exactly one line
if two lines intersect then their intersection is exactly one…
through any three non collinear points there exists exactly o…
a plane contains at least three non collinear points
two point postulate/line point postulate
through any two points there exists exactly one line
line intersection postulate
if two lines intersect then their intersection is exactly one…
8 terms
Postulates
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any 2 points there is exactly one line
Through any 3 non collinear points there is exactly 1 plane
A line contains at least 2 points
A plane contains at least three non collinear points
Postulate 2.1
Through any 2 points there is exactly one line
Postulate 2.2
Through any 3 non collinear points there is exactly 1 plane
Postulates
1.1 Ruler Postulate
1.2 Segment Addition Postulate
1.3 Protractor Postulate
1.4 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.... If AB + BC =AC, t…
Consider line OB and a point A on one side of line OB. The ra…
If P is in the interior of andgle RST, then the measure of an…
1.1 Ruler Postulate
The points on a line can be matched one to one with the real…
1.2 Segment Addition Postulate
If B is between A and C, then AB + BC = AC.... If AB + BC =AC, t…
11 terms
Postulates
1 Ruler Postulate
2 Segment Addition Postulate
3 Protractor Postulate
4 Angle Addition Postulate
The points on a line can be matched one to one with the real…
When 3 points are collinear, you can say one point is between…
The measurement of a angle between two rays can be designated…
If a point is in the interior of an angle, the measure of the…
1 Ruler Postulate
The points on a line can be matched one to one with the real…
2 Segment Addition Postulate
When 3 points are collinear, you can say one point is between…
postulates
postulate 5
postulate 6
postulate 7
postulate 8
Through any two points there is exactly one line
A line contains at least 2 points
If two lines intersect, then their intersection is exactly on…
Through any 3 non-collinear points there exist exactly one pl…
postulate 5
Through any two points there is exactly one line
postulate 6
A line contains at least 2 points
10 terms
Postulates
3.1 Corresponding Angles Postulate
3.2 Slopes of Parallel Lines Postulate
3.3 Slopes of Perpendicular Lines Post…
3.4 Converse of Corresponding Angles P…
if two parallel lines are cut by a transversal, then each pai…
two non vertical lines have the same slope if and only if the…
two non vertical lines are perpendicular if and only if the p…
if two lines are cut by a transversal so that corresponding a…
3.1 Corresponding Angles Postulate
if two parallel lines are cut by a transversal, then each pai…
3.2 Slopes of Parallel Lines Postulate
two non vertical lines have the same slope if and only if the…
15 terms
Postulates
Through two distinct points, there is…
The measure of any line segment is a u…
If X is a point of segment AB and A-X-…
If two lines intersect, they intersect…
Postulate 1
Postulate 2: Ruler Postulate
Postulate 3: Segment-Addition Postulate
Postulate 4
Through two distinct points, there is…
Postulate 1
The measure of any line segment is a u…
Postulate 2: Ruler Postulate
14 terms
Postulates
Ruler Postulate (Postulate 1)
Segment Addition Postulate (Postulate 2)
Protractor Postulate (Postulate 3)
Angle Addition Postulate (Postulate 4)
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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.
Ruler Postulate (Postulate 1)
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate (Postulate 2)
If B is between A and C, then AB+BC=AC.
11 terms
Postulates
RULER POSTULATE
SEGMENT ADDITION POSTULATE
PROTRACTOR POSTULATE
ANGLE ADDITION POSTULATE
On a number line, every point can be paired with a number and…
RULER POSTULATE
On a number line, every point can be paired with a number and…
SEGMENT ADDITION POSTULATE
12 terms
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 Ray Ob. ... The ray…
If P is in the interior of ∠RST, then m∠RST = m∠RST + m∠PST.
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,…
9 terms
Postulates
Ruler postulate
Segmant addition postulate
Angle addition postulate
Unnamed
Ruler postulate
Segmant addition postulate
9 terms
Postulates
Segment Addition Postulate
Angle Addition Postulate
Postulate 5
Postulate 6
If B is between A and C, then AB+BC = AC
if B is the interior of angle AOC, then the measure of angle…
a line contains at least two points, a plane contains at leas…
through any two points, there is exactly one line
Segment Addition Postulate
If B is between A and C, then AB+BC = AC
Angle Addition Postulate
if B is the interior of angle AOC, then the measure of angle…
9 terms
Postulates
If given two points, then there is exa…
If given three non-collinear points, t…
If given a line, then it contains at l…
If given a plane, then it contains at…
If given two points, then there is exa…
If given three non-collinear points, t…
5 terms
Postulates
parallel postulate
perpendicular postulate
translation postulate
reflection postulate
if there is a line and a point not on the line, then there is…
If there is a line and a point not on the line, then there is…
a translation is a rigid motion
a reflection is a rigid motion
parallel postulate
if there is a line and a point not on the line, then there is…
perpendicular postulate
If there is a line and a point not on the line, then there is…
21 terms
Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
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.
xxx Given a point, X, on PR, consider XP and XR, as well as a…
xxx If point D is in the interior of ABC, then m ABD + m DBC…
Ruler Postulate
The points on a line can be paired in a one to one correspond…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
9 terms
Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
1) Scale- can match points on line with numbers... 2) Distance b…
If B is between A and C then AB+BC=AC
1) Scale... 2) Angle measure
1) If D is in the interior of angle ABC, then the measure of…
Ruler Postulate
1) Scale- can match points on line with numbers... 2) Distance b…
Segment Addition Postulate
If B is between A and C then AB+BC=AC
8 terms
Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 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
Through any two points there is exactly one line
Postulate 2
If two distinct lines intersect, then they intersect in exact…
9 terms
Postulates
Segment Addition Postulate
Angle Addition Postulate
Two Point Postulate
Line-Point Postulate
If C is between A and B, then AC+BC=AC.
If ray B is a segment bisector of ∠ABC, then m∠AOB + m∠BOC =…
Through any two points there exists exactly 1 line
A line contains at least 2 points
Segment Addition Postulate
If C is between A and B, then AC+BC=AC.
Angle Addition Postulate
If ray B is a segment bisector of ∠ABC, then m∠AOB + m∠BOC =…
18 terms
Postulates
2.1
2.2
2.3
2.4
Through any 2 points, there is exactly one 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 one line
2.2
Through any 3 noncollinear points, there is exactly 1 plane
19 terms
Postulates
Postulate
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 3: Protractor Postulate
A statement that is accepted as true without proof.
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
The measurement of an angle between two rays can be designate…
Postulate
A statement that is accepted as true without proof.
Postulate 1: Ruler Postulate
The points on a line can be put into a one-to-one corresponde…
9 terms
Postulates
Distance Postulate
Ruler Postulate
Ruler Placement Postulate
The Line Postulate
To every pair of different points there corresponds a unique…
The points of a line can be placed in correspondence with the…
Given two points P and Q of a line, the coordinate system can…
For every two points there is exactly one line that contains…
Distance Postulate
To every pair of different points there corresponds a unique…
Ruler Postulate
The points of a line can be placed in correspondence with the…
17 terms
Postulates
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 cannot equal 0
Addition Property of Equality
If a=b, then a+c = b+c
Subtraction Property of Equality
If a=b, then a-c = b-c
14 terms
Postulates
Ruler Postulate (Postulate 1)
Segment Addition Postulate (Postulate 2)
Protractor Postulate (Postulate 3)
Angle Addition Postulate (Postulate 4)
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 lie in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC.
Ruler Postulate (Postulate 1)
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate (Postulate 2)
If B is between A and C, then AB+BC=AC.
11 terms
Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
points on a line can be matched one to one with real numbers
if B is between A and C, then AB+BC= AC
the measure of aoc is equal to the absolute value of the dist…
if b is the interior of coa, then the measure of coa= the mea…
Postulate 1
points on a line can be matched one to one with real numbers
Postulate 2
if B is between A and C, then AB+BC= AC
7 terms
Postulates
through any two points
through any three noncollinear points
if two points lie on a plane
the intersection of two lines
there is exactly one line
there is exactly one plane
then the line containing those points is also on the plane
is exactly one point
through any two points
there is exactly one line
through any three noncollinear points
there is exactly one plane
36 terms
Postulates
Ruler Postulate
Segment Addition Postulate
Distance Formula
Protractor Postulate
the points on a line can be matched one to one with real numb…
B is between A and C iff A B + B C = A C
The rays in a half rotation can be numbered from 0 to 180. Th…
Ruler Postulate
the points on a line can be matched one to one with real numb…
Segment Addition Postulate
B is between A and C iff A B + B C = A C
11 terms
Postulates
1-1-1... Points, Lines, and Planes
1-1-2... Points, Lines, and Planes
1-1-3... Points, Lines, and Planes
1-1-4... Intersection of lines and planes
Through any two points there is exactly one line
Through any three noncollinear points there is exactly one pl…
If two points lie in a plane, then the line containing those…
if two lines intersect, then they intersect in exactly one po…
1-1-1... Points, Lines, and Planes
Through any two points there is exactly one line
1-1-2... Points, Lines, and Planes
Through any three noncollinear points there is exactly one pl…
24 terms
Postulates
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Postulate
Corresponding Angles Converse
If there is a line and a point not on the line, then there is…
If there is a line and a point not on the line, then there is…
If two lines are cut by a transversal so that the correspondi…
If two lines are cut by a transversal, then the pairs of corr…
Parallel Postulate
If there is a line and a point not on the line, then there is…
Perpendicular Postulate
If there is a line and a point not on the line, then there is…
6 terms
postulates
SSS theorem
SAS theorem
AA similarity postulate
triangle midsegment theorem
If the corresponding side lengths of 2 triangles are proporti…
If the lengths of 2 corresponding sides of another triangle a…
if 2 angles of one triangle are congruent to 2 angles of anot…
A midsegment of a triangle is parallel to a side of the trian…
SSS theorem
If the corresponding side lengths of 2 triangles are proporti…
SAS theorem
If the lengths of 2 corresponding sides of another triangle a…
19 terms
Postulates
2.1
2.2
2.3
2.4
Through any two points 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 non collinear points
2.1
Through any two points is exactly one line.
2.2
Through any three non collinear points, there is exactly one…
8 terms
Postulates
Ruler Postulate
Protractor Postulate
Angle Addition Postulate
Segment Addition Postulate
The ruler postulate tells us how to find the distance between…
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…
The segment addition postulate is a fairly obvious-seeming po…
Ruler Postulate
The ruler postulate tells us how to find the distance between…
Protractor Postulate
Given line AB and a point O on line AB. Consider rays OA and…
Postulates
postulate 1
postulate 2
postulate 3
postulate 4
through any two points there is exactly one line.
through any three non-collinear points there is exactly one p…
a line contains at least two points
a plane contains at least three non-collinear points.
postulate 1
through any two points there is exactly one line.
postulate 2
through any three non-collinear points there is exactly one p…
11 terms
Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
On a number line, every point can be paired with a number and…
The distance from one endpoint to the other is the sum of the…
Given line AB and a point O on line AB. Consider rays OA and…
The measure of the larger angle is the sum of the measures of…
Ruler Postulate
On a number line, every point can be paired with a number and…
Segment Addition Postulate
The distance from one endpoint to the other is the sum of the…
8 terms
postulates
ruler postulate
protracture postulate
Angle addition postulate
segment addition postulate
Ruler Postulate Summary. On a number line, every point can be…
The Protractor Postulate. Given line AB and a point O on line…
The angle addition postulate states that if B is in the inter…
The segment addition postulate is a fairly obvious-seeming po…
ruler postulate
Ruler Postulate Summary. On a number line, every point can be…
protracture postulate
The Protractor Postulate. Given line AB and a point O on line…
8 terms
Postulates
P5
P6
P7
P8
Through only two points,there is exactly one line. ... If you h…
A line contains at least two points. If you have a line, then…
If two lines intersect, then their intersection is exactly on…
Through any three non-collider points, there is exactly one p…
P5
Through only two points,there is exactly one line. ... If you h…
P6
A line contains at least two points. If you have a line, then…
14 terms
Postulates
Properties of Equality
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Let a, b, and c be real numbers
If a = b, then a + c = b + c
If a = b, then a - c = b - c
If a=b, then ac= bc
Properties of Equality
Let a, b, and c be real numbers
Addition property of equality
If a = b, then a + c = b + c
11 terms
Postulates
Corresponding angles theorem
Alternate interior angles theorem
Alternate exterior angles
Same side interior angles theorem
If two lines are cut by a transveral then the pairs if corr a…
If parallel then alt int angles congruent
If parallel cut by a transversal then alt ext angles congruent
If parallel same side interior angles supp
Corresponding angles theorem
If two lines are cut by a transveral then the pairs if corr a…
Alternate interior angles theorem
If parallel then alt int angles congruent
12 terms
postulates
ruler postulate
segment postulate
Protractor postulate
angle addition postulate
|b-a|
st+tu=su
mpas < 5
M< ABD + M<DBC = M<ABC
ruler postulate
|b-a|
segment postulate
st+tu=su
17 terms
Postulates
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 cannot equal 0
Addition Property of Equality
If a=b, then a+c = b+c
Subtraction Property of Equality
If a=b, then a-c = b-c
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