Study sets matching "geometry theorems postulates"

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Study sets matching "geometry theorems postulates"

42 terms
Postulates/Theorems for Geometry
Addition Propery 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 a•c=b•c
If a=b, then a÷c=b÷c
Addition Propery of Equality
If a=b, then a+c=b+c
Subtraction Property of Equality
If a=b, then a-c=b-c
16 terms
geometry theorems and postulates
if M is the midpoint of AB
through a line and a point not in the…
if two lines intersect
if BX is the bisector of angle ABC
AM = 1/2AB and MB = 1/2 AM
there is exactly one plane
exactly one plane contains the lines
measurement of angle ABX = 1/2 measurement of angle ABC
if M is the midpoint of AB
AM = 1/2AB and MB = 1/2 AM
through a line and a point not in the…
there is exactly one plane
35 terms
Geometry - Postulates, Theorems, & Properties
Postulate 5
Postulate 6
Postulate 8
Postulate 9
Through any 2 points there exists exactly one line
A line contains at least 2 points
Through any 3 non-collinear points there exists exactly one p…
A plane contains at least 3 noncollinear points
Postulate 5
Through any 2 points there exists exactly one line
Postulate 6
A line contains at least 2 points
27 terms
Geometry Postulates and Theorems
Unique line postulate
Unique plane postulate
Dimension assumption postulates
Line intersection postulate
Through any two points, there exists exactly one line
Through any three non-collinear points, there exists exactly…
-Given a line, there exists at least one point not on the lin…
If two lines intersect, then they intersect at exactly one po…
Unique line postulate
Through any two points, there exists exactly one line
Unique plane postulate
Through any three non-collinear points, there exists exactly…
42 terms
Geometry: Theorems, Postulates, and Terms
Vertical Angle Theorem
Adjacent Angle
Complementary Angle
Supplementary angle
Vertical Angles are congruent
A pair of angles in the same plane that meet the following co…
2 angles whose measures add up to 90 degrees
2 angles whose measures add up to 180 degrees
Vertical Angle Theorem
Vertical Angles are congruent
Adjacent Angle
A pair of angles in the same plane that meet the following co…
Postulates and Theorems-Geometry
Ruler postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
Points on a line can be matched one to one with the real numb…
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 lineOB. The rays of the for…
If P is in the interior of angleRST, then the measure-angleRS…
Ruler postulate
Points on a line can be matched one to one with the real numb…
Segment addition postulate
If B is between A and C, then AB+BC=AC. If AB+BC=AC. Then B i…
Geometry Definitions, Postulates, and Theorems.
Segment congruence postulate
Segment addition postulate
Angle congruence postulate
Angle addition postulate
If two segements have the same length as measured by a fair r…
If point R is between points P and Q on a line then; PR + RQ…
If two angles have the same measure, then they are congruent.…
If point S is in the interior of angle PQR, then the measure…
Segment congruence postulate
If two segements have the same length as measured by a fair r…
Segment addition postulate
If point R is between points P and Q on a line then; PR + RQ…
129 terms
Geometry theorems and 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 the AB + BC = AC. IF AB + BC = AC, th…
Consider OB and a point A on one side of OB. The rays of the…
If P is in the interior of < RST, then the measure of <RST is…
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 the AB + BC = AC. IF AB + BC = AC, th…
47 terms
geometry ac theorems & postulates
angle addition postulate
right angles congruence theorem
APOE
SPOE
if P is the interior of angle RST, then the measure of RST is…
all right angles are congruent
if a=b, then a+c=b+c
if a=b, then a-c=b-c
angle addition postulate
if P is the interior of angle RST, then the measure of RST is…
right angles congruence theorem
all right angles are congruent
Geometry Theorems/Postulates/Corollaries
Linear Pair Postulate
Corresponding Angles Postulate
Two Perps Theorem
Perpendicular Transversal Theorem
If two angles form a linear pair, then they are supplementary.
If two parallel lines are cut by a transversal, then the pair…
If two lines are perpendicular to the same line, then the lin…
If a line is perpendicular to one of two parallel lines, then…
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pair…
geometry postulates/theorems
postulate
theorem
postulate(1)
postulate(2)
a basic assumption accepted without proof
a statement that can be proved using postulates, definitions,…
a line contains at least 2 points, a plane contains at least…
through any 2 points, there is exactly one line
postulate
a basic assumption accepted without proof
theorem
a statement that can be proved using postulates, definitions,…
10 terms
Geometry Theorems and Postulates
Linear Pair Theorem
Congruent Supplement Theorem
Right Angle Congruence Theorem
Congruent Complementary Theorem
If two angles form a linear pair, then they are supplementary.
If two angles are supplementary to the same angle (or to two…
All right angles are congruent
If two angles are complementary to the same angle (or two con…
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Congruent Supplement Theorem
If two angles are supplementary to the same angle (or to two…
80 terms
Geometry - 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 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…
Geometry theorems and postulates
point
line
plane
collinear points
spot;an object with no dimension
straight; an object that extends infinitely
flat;extends infinitely in two dimension
points that lie on the same line
point
spot;an object with no dimension
line
straight; an object that extends infinitely
35 terms
Geometry Theorems, Definitions, and postulates
Complementary Angles
Supplementary angles
theorem
Vertical angles
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 degrees
a statement that can be proven
4 angles formed by intersecting lines and facing in four diff…
Complementary Angles
Two angles whose measures equal 90 degrees
Supplementary angles
two angles whose measures equal 180 degrees
10 terms
Geometry Theorems and Postulates
Side-Side-Side Postulate... (SSS)
Side-Angle-Side Postulate... (SAS)
Angle-Side-Angle Postulate... (ASA)
Angle-Angle-Side Theorem... (AAS)
If three sides of one triangle are congruent to three of anot…
If two sides and the included angle of one triangle are congr…
If two angles and the included side of one triangle are congr…
If two angles and a non included side of one triangle are con…
Side-Side-Side Postulate... (SSS)
If three sides of one triangle are congruent to three of anot…
Side-Angle-Side Postulate... (SAS)
If two sides and the included angle of one triangle are congr…
10 terms
geometry postulates and theorems
postulate
theorem
postulate 5
postulate 6
a statement accepted without proof
a statement that requires proof
a line contains at least two points, a plane contains at leas…
through any two points there is exactly one line
postulate
a statement accepted without proof
theorem
a statement that requires proof
9 terms
Geometry Theorems and Postulates
PBT
CPBT
RAT
≅ST
Perpendicular Bisector Theorem: If two points are equidistant…
Converse Perpendicular Bisector Theorem: If a point is on per…
Right Angle Theorem: If two angles are both congruent and sup…
Congruent Supplement Theorem: If two angles are congruent, th…
PBT
Perpendicular Bisector Theorem: If two points are equidistant…
CPBT
Converse Perpendicular Bisector Theorem: If a point is on per…
8 terms
Geometry Theorems and Postulates
Ruler Postulate
Protractor Postulate
Angle Addition Postulate
Linear Pair Postulate
Once a coordinate system has been chosen in this way, the dis…
the measure of an angle is equal to the absolute value of the…
add two angles together, you get a bigger angle, same vertex…
If two angles form a linear pair, then they are supplementary
Ruler Postulate
Once a coordinate system has been chosen in this way, the dis…
Protractor Postulate
the measure of an angle is equal to the absolute value of the…
27 terms
Geometry Postulates and Theorems
expansion
line
flat plane
plane intersection
Which postulate states that a line contains at least two poin…
Which postulate states that any two points in space lie in ex…
Which postulate states if two points lie in a plane, then the…
Which postulate states if two planes intersect, then their in…
expansion
Which postulate states that a line contains at least two poin…
line
Which postulate states that any two points in space lie in ex…
7 terms
Geometry Postulates/Theorems/Definitions
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Postulate
Subtractive Property of equality
If point B lies on a line segment AC then AB+BC= AC
Variable that lies on the interior of angle then add the degr…
Two angles are a linear pair if the angles are adjacent and t…
States that when both sides of an equation have the same numb…
Segment Addition Postulate
If point B lies on a line segment AC then AB+BC= AC
Angle Addition Postulate
Variable that lies on the interior of angle then add the degr…
19 terms
Geometry Postulates/Theorems/Properties
Linear Pair Postulate
Segment Addition Postulate
Angle Addition Postulate
Addition Property
If two angles form a linear pair, then they are supplementary
If you have a line made up of pieces, add the small pieces to…
If P is in the interior of <RST, then m<RSP + m<PST = m<RST (…
If you add the same numbers to each side of an equation, both…
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary
Segment Addition Postulate
If you have a line made up of pieces, add the small pieces to…
17 terms
Geometry Theorems and Postulates
Segment Addition Postulate
Angle Addition Postulate
Protractor Postulste
Ruler Postulate
If B is between A and C then AB + BC = AC. If AB + BC = AC ,…
If B is the Interior of < COA, then m< COB + m< BOA = m< COA
Given line AB and a point O on line AB. Consider rays OA and…
On a number line, every point can be paired with a number and…
Segment Addition Postulate
If B is between A and C then AB + BC = AC. If AB + BC = AC ,…
Angle Addition Postulate
If B is the Interior of < COA, then m< COB + m< BOA = m< COA
43 terms
Geometry Theorems and Postulates
Congruent Supplements Theorem
Congruent Complements Theorem
Linear Pair Postulate
Vertical Angle Theorem
If two angles are supplementary to the same or congruent angl…
If two angles are complementary to the same or congruent angl…
If two angles form a linear pair, then they are supplementary
Vertical angles are congruent
Congruent Supplements Theorem
If two angles are supplementary to the same or congruent angl…
Congruent Complements Theorem
If two angles are complementary to the same or congruent angl…
12 terms
Geometry Postulates and Theorems
Postulate 1 :Ruler
Postulate 2: Segment Addition
Postulate 3: Protractor
Postulate 4: Angle Addition
1: The point on a line can be paired with the real numbers in…
if B is between A and C then AB + BC= AC
1:How to set up a protractor... 2:How to measure an angle
Angles have to add up to 180º
Postulate 1 :Ruler
1: The point on a line can be paired with the real numbers in…
Postulate 2: Segment Addition
if B is between A and C then AB + BC= AC
23 terms
Geometry Postulates and Theorems
Side-Angle-Side (SAS) Congruence Postu…
Side-Side-Side (SSS) Postulate
Angle-Side-Angle (ASA) Postulate
Angle-Angle-Side (AAS) Theorem
In one triangle, if two sides and the angle between those sid…
If the three sides of one triangle are congruent to the three…
If two angles and the included side of one triangle are congr…
If two angles and a non-included side of one triangle are con…
Side-Angle-Side (SAS) Congruence Postu…
In one triangle, if two sides and the angle between those sid…
Side-Side-Side (SSS) Postulate
If the three sides of one triangle are congruent to the three…
8 terms
Geometry Theorems and Postulates
Pythagorean Theorum
Converse of Pythagorean Theorem
If two angles are right angles then th…
If two angles are straight angles then…
A^2+B^2=C^2
If A^2+B^2=C^2 then it's a right triangle.... If it's a right tr…
If two angles have the same measure then they are congruent
If two angles have the same measure then they are congruent
Pythagorean Theorum
A^2+B^2=C^2
Converse of Pythagorean Theorem
If A^2+B^2=C^2 then it's a right triangle.... If it's a right tr…
33 terms
Geometry Postulates, Theorems, Definitions, etc.
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 is the absolute value of…
If B is in between A and C, then AB+BC=AC
The measure of angle AOB is equal to the absolute value of th…
If point B is in the interior of angle COA, then the measure…
Postulate 1 (Ruler Postulate)
The distance between points a and b is the absolute value of…
Postulate 2 (Segment Addition Postulate)
If B is in between A and C, then AB+BC=AC
121 terms
Geometry Postulates, Theorems, and Definitions
Segment Addition Postulate
Protractor Postulate
Parallel Lines
Skew Lines
AB + BC = AC
Says that you can measure any angle
two lines that don't intersect and are coplanar
two lines that don't intersect and aren't coplanar
Segment Addition Postulate
AB + BC = AC
Protractor Postulate
Says that you can measure any angle
Geometry Theorems and Postulates
HL Theorem
AAS Theorem
ASA Postulate
SAS Postulate
If the two hypotenuse and a leg of one triangle are congruent…
If two angels and a non included side of one triangle are con…
If two angles and the included side of one triangle are congr…
If two sides and the included angle of one triangle are congr…
HL Theorem
If the two hypotenuse and a leg of one triangle are congruent…
AAS Theorem
If two angels and a non included side of one triangle are con…
16 terms
Geometry Theorems, Postulates, and Vocabulary.
Reflexive
Symmetric
Transitive
Segment Addition Postulate
Line segment AB is congruent to line segment CD
If line segment AB is congruent to line segment CD, then line…
If line segment AB is congruent to line segment CD, and line…
Two segments of a line added together to get the length of th…
Reflexive
Line segment AB is congruent to line segment CD
Symmetric
If line segment AB is congruent to line segment CD, then line…
32 terms
Geometry Postulates & Theorems
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Postulate
Parallel Postulate
If B is between = A & C then, AB + BC = AC. Then B is the mid…
If P is in the interior of <RST, Then m<RST = m<RSP + m<PST
If two angles form a linear pair, then they are supplementary
If there is a line and a point not on a line, then there is e…
Segment Addition Postulate
If B is between = A & C then, AB + BC = AC. Then B is the mid…
Angle Addition Postulate
If P is in the interior of <RST, Then m<RST = m<RSP + m<PST
37 terms
Geometry postulates and theorems
Corresponding angles
alternate interior angles
alternate exterior angles
consecutive interior angles
if 2 parallel lines are cut by a transversal, then the pairs…
if 2 angles lie between the 2 lines and on opposite sides of…
if 2 angles lie outside the 2 lines and on opposite sides of…
if 2 angles lie between the 2 lines and on the same side of t…
Corresponding angles
if 2 parallel lines are cut by a transversal, then the pairs…
alternate interior angles
if 2 angles lie between the 2 lines and on opposite sides of…
17 terms
Geometry Postulates and Theorems
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 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 the real…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC,…
58 terms
Geometry Theorems, Definitions, and postulates
Complementary Angles
Supplementary angles
theorem
Vertical angles
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 d
a statement that can be proven
4 angles formed by intersecting lines and facing in four diff…
Complementary Angles
Two angles whose measures equal 90 degrees
Supplementary angles
two angles whose measures equal 180 d
62 terms
Geometry Postulates and Theorems
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
geometry postulates/theorems
Line tangent to circle→Line perpendicu…
Line perpendicular to radius→line tang…
2 segments tangent to circle from same…
Arc addition postulate
If a line is tangent to a circle, then the line is perpendicu…
If a line is perpendicular to the radius, then it is tangent…
If two segments are tangent to a circle from the same externa…
the measure of an arc formed by two adjacent arcs is the sum…
Line tangent to circle→Line perpendicu…
If a line is tangent to a circle, then the line is perpendicu…
Line perpendicular to radius→line tang…
If a line is perpendicular to the radius, then it is tangent…
Geometry Postulates and Theorems
Parallel lines
Skew lines
Transversal
Corresponding Angles
coplanar lines that never intersect
lines that never intersect and noncoplanar
is a line in a plane that intersects at least two coplanar li…
angles in corresponding position
Parallel lines
coplanar lines that never intersect
Skew lines
lines that never intersect and noncoplanar
Geometry Postulates, Theorems, and Definitions
Segment Addition Postulate
Protractor Postulate
Parallel Lines
Skew Lines
AB + BC = AC
Says that you can measure any angle
two lines that don't intersect and are coplanar
two lines that don't intersect and aren't coplanar
Segment Addition Postulate
AB + BC = AC
Protractor Postulate
Says that you can measure any angle
10 terms
Geometry Theorems and Postulates
Postulate 1: the distance postulate
Postulate 2: the ruler postulate
Postulate 3: the ruler placement postu…
Postulate 4: 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…
Postulate 1: the distance postulate
To every pair of different points there corresponds a unique…
Postulate 2: the ruler postulate
the points of a line can be placed in correspondence with the…
geometry theorems and postulates
2 points determine
2 lines intersect in
2 planes intersect in
3 points determine
exactly one line
exactly one point
exactly one line
a plane
2 points determine
exactly one line
2 lines intersect in
exactly one point
42 terms
Geometry Theorems and Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
pints on a line can be parried with real numbers so that any…
If B is between A and C, then AB + BC =AC
Given line AB and a point O on line AB. Consider rays OA and…
Angle 1 + Angle 2 = Angle 1+2
Ruler Postulate
pints on a line can be parried with real numbers so that any…
Segment Addition Postulate
If B is between A and C, then AB + BC =AC
44 terms
Geometry Vocab, Postulates, & Theorems
Point
Line
Line Segment
Ray
Indicates a location
represented by a straight path that extends in 2 opposite dir…
Part of a line that contains 2 endpoints
Part of a line that consists of 1 endpoint and all points tha…
Point
Indicates a location
Line
represented by a straight path that extends in 2 opposite dir…
63 terms
Geometry Theorems & Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points, there is exactly one line.
Lines can only intersect at exactly one point.
Planes can only intersect at exactly one line.
Through any three non-collinear points, there is exactly one…
Postulate 1-1
Through any two points, there is exactly one line.
Postulate 1-2
Lines can only intersect at exactly one point.
74 terms
Geometry Definitions,Postulates and Theorems
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
31 terms
Geometry Postulates & Theorems
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 A and C then AB+BC=AC
: On line AB of a given plane, choose any point between A and…
If point B lies in the interior of angle AOC then m angle AOB…
Ruler Postulate:
The points on a line can be paired with the real numbers in s…
Segment Addition Postulate:
If B is A and C then AB+BC=AC
49 terms
Geometry Theorems & Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points, there is exactly one line.
Lines can only intersect at exactly one point.
Planes can only intersect at exactly one line.
Through any three non-collinear points, there is exactly one…
Postulate 1-1
Through any two points, there is exactly one line.
Postulate 1-2
Lines can only intersect at exactly one point.
49 terms
Geometry Theorems & Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points, there is exactly one line.
Lines can only intersect at exactly one point.
Planes can only intersect at exactly one line.
Through any three non-collinear points, there is exactly one…
Postulate 1-1
Through any two points, there is exactly one line.
Postulate 1-2
Lines can only intersect at exactly one point.
84 terms
Geometry Theorems and Postulates
Line Intersection Theorem
Linear Pair Theorem
Vertical Angles Theorem
Corresponding Angles Postulate
Two different lines intersect in at one point.
If two angels form a linear pair, then they are supplementary.
If two angles are vertical angles then they have equal measur…
If two angles have the same measure then they are parallel. I…
Line Intersection Theorem
Two different lines intersect in at one point.
Linear Pair Theorem
If two angels form a linear pair, then they are supplementary.
12 terms
Geometry Theorems and Postulates
side XY is congruent to side XZ
Triangle Sum Thm.
Isosceles Triangle Thm.
two congruent sides
Since XY equals XZ
M<X + M<Y + M<Z = 180
base angles Z & Y are congruent so m<Z = M<Y
Isosceles Triangles have at least
side XY is congruent to side XZ
Since XY equals XZ
Triangle Sum Thm.
M<X + M<Y + M<Z = 180
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