Study sets matching "geometry postulates theorems postulates definitions"

Study sets
Classes
Users

Study sets matching "geometry postulates theorems postulates definitions"

14 terms
Geometry Theorems/Definitions/Postulates
Linear Pairs are Supplementary.
Perpendicular Lines form right angles.
All right angles are congruent.
Supplements of congruent angles are co…
Right
Supplementary (Working with total of 4 angles)
Linear Pairs are Supplementary.
Perpendicular Lines form right angles.
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°
39 terms
Geometry Theorems, Postulates, & Definitions
Segment Addition Postulate
Angle Addition Postulate
Definition of Midpoint & Bisector
Definition of Angle Bisector
If B is between A and C then the length of AC is equal to the…
If P is in the interior of ∠RST then the measure of ∠RST is t…
A bisector bisects a line segment at its midpoint which divid…
A ray that divides an angle into two adjacent angles that are…
Segment Addition Postulate
If B is between A and C then the length of AC is equal to the…
Angle Addition Postulate
If P is in the interior of ∠RST then the measure of ∠RST is t…
25 terms
Geometry Definitions/Theorems/Postulates
Midpoint
Collinear
Straight Angles
Acute Angles
It is a midpoint if and only if it divides a segment into two…
3 or more points on the same line
The sides of a straight angle form a line
Acute angles are less than a right angle
Midpoint
It is a midpoint if and only if it divides a segment into two…
Collinear
3 or more points on the same line
50 terms
Theorems/Postulates/Definition Geometry
Ruler Postulate
Segment 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 line AB in a given plane, choose any point O between A and…
If point B lies in the interior of <AOC, the m<AOB a m<BOC =…
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
74 terms
Geometry Definitions, Postulates and Theorems
Complementary angles
Supplementary angles
Theorem
Vertical Angles
two angles whose measures have a sum of 90°
two angles who measures have a sum of 180°
a statement that can be proven
two angles formed by intersecting lines and facing in the opp…
Complementary angles
two angles whose measures have a sum of 90°
Supplementary angles
two angles who measures have a sum of 180°
Geometry: postulates, theorems, and definitions
Segment addition postulate
Angle addition postulate
Postulate 5
Postulate 6
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 =…
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 point B lies in the interior of <AOC, then m<AOB + m<BOC =…
Geometry - Theorems, Postulates, and Definitions
Linear Pair Postulate
Law of Detachment (word definition)
Law of Detachment (symbolic form)
Law of Syllogism (symbolic form)
If two angles form a linear pair, then they are supplementary.
If the hypothesis of a true conditional is true, then the con…
If p --> q is true and p is true, then q is true.
If p --> q is true and q --> r is true, then p --> r is true.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Law of Detachment (word definition)
If the hypothesis of a true conditional is true, then the con…
Geometry Postulates, Theorems, and Definitions
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 AND c≠0, then a/c=b/c
addition property of equality
if a=b, then a+c=b+c
subtraction property of equality
if a=b, then a-c=b-c
20 terms
Geometry Definitions, Postulates and Theorems
Definition of Midpoint
Vertical Angles Theorem
Reflexive property
Symmetric property
(Not def. Of congruent segments)
∠CXE=∠CXE
GH = KL so ... KL = GH
Definition of Midpoint
(Not def. Of congruent segments)
Vertical Angles Theorem
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, Postulates, and Definitions
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 real numbers in such…
If B is between A and C, then AB+ BC= AC
If in <QOA, Ray OP lies inside of the angle, ... <QOP=<QOA-<POA
If point B lies on the interior of angle AOC, then angle AOB+…
Postulate 1 (Ruler Postulate)
The points on a line can be paired with real numbers in such…
Postulate 2 (Segment Addition Postulate)
If B is between A and C, then AB+ BC= AC
63 terms
Geometry Theorems/Postulates/Definitions
theorem
postulate
definition
segment bisector
a statement that can be proved
something we don't need to prove, uses past information to ba…
assigns a term to an object. are always reversible
segment,ray,line, plane that divides a segment into two congr…
theorem
a statement that can be proved
postulate
something we don't need to prove, uses past information to ba…
Geometry Definitions, Postulates and Theorems
Definition of Midpoint
Vertical Angles Theorem
Reflexive property
Symmetric property
(Not def. Of congruent segments)
∠CXE=∠CXE
GH = KL so ... KL = GH
Definition of Midpoint
(Not def. Of congruent segments)
Vertical Angles Theorem
81 terms
Geometry Theorems/Postulates/Definitions
theorem
postulate
definition
geometry
a statement that can be proved
something we don't need to prove, uses past information to ba…
assigns a term to an object. are always reversible
to take a series of facts to put in a logical way to reach a…
theorem
a statement that can be proved
postulate
something we don't need to prove, uses past information to ba…
72 terms
Geometry Theorems, Definitions, and postulates
Definitions
Complementary Angles
Supplementary angles
theorem
Definitions
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 degrees
a statement that can be proven
Definitions
Definitions
Complementary Angles
Two angles whose measures equal 90 degrees
63 terms
Geometry Theorems, Postulates, and Definitions
Parallel Lines
Perpendicular Lines
Skew Lines
Parallel Planes
Are coplanar lines and do not intersect.
Lines that intersect at 90 degree angles.
Lines that are not coplanar, not parallel, and do not interse…
Are planes that do not intersect.
Parallel Lines
Are coplanar lines and do not intersect.
Perpendicular Lines
Lines that intersect at 90 degree angles.
72 terms
Geometry Theorems, Definitions, and postulates
Definitions
Complementary Angles
Supplementary angles
theorem
Definitions
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 degrees
a statement that can be proven
Definitions
Definitions
Complementary Angles
Two angles whose measures equal 90 degrees
68 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
26 terms
Geometry Definitions, Postulates and Theorems
Complementary Angles
Supplementary Angles
Theorem
Vertical Angles
Two angles whose measures have a sum of 90
Two angles whose measures have a sum of 180
A statement that can be proven
Tow 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 whose measures have a sum of 180
14 terms
Geometry- Definitions, Postulates and Theorems
Perpendicular Lines
Angle Bisector
Midpoint
Congruent Angles
two lines that intersect to form right angles
The ray that divides the angle into two congruent adjacent an…
The point that divides the segment into two congruent segments
Angles that have equal measure
Perpendicular Lines
two lines that intersect to form right angles
Angle Bisector
The ray that divides the angle into two congruent adjacent an…
14 terms
geometry definitions, theorems, postulates
complementary angles
congruent angles
congruent complements theorem
congruent segments
two angles whose measures have a sum of 90 degrees
angles that have the same measure
if two angles are complementary to the same angle or to congr…
segments have the same length
complementary angles
two angles whose measures have a sum of 90 degrees
congruent angles
angles that have the same measure
27 terms
Geometry Definitions, Postulates, and Theorems
Vertical Angles
Angle Bisector
Segment Bisector
Midpoint
Two angles whose sides form two pairs of opposite rays.
A ray that divides an angle into two adjacent angles that are…
Anything that intersects a segment at its midpoint.
The point that divides or bisects a segment into two congruen…
Vertical Angles
Two angles whose sides form two pairs of opposite rays.
Angle Bisector
A ray that divides an angle into two adjacent angles that are…
60 terms
Geometry: Postulates/Theorems/Definitions/
Segment Addition Postulate
Definition of Congruent Angles/Segments
Definition of a Midpoint
Definition of Bisector
If B is between A and C, then AB + BC = AC
Angles/Segments of Equal Length
Point that is the middle of two congruent segments
Line/segment/ray/plane that intersects the segment at its mid…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Definition of Congruent Angles/Segments
Angles/Segments of Equal Length
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
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…
Geometry Definitions, Postulates, and Theorems
Addition Property
Subtraction Property
Multiplication Property
Division Property
Adding on both sides of the equal sign
Subtracting on both sides of the equal sign
Multiplying on both sides of the equal sign
Dividing on both sides of the equal sign
Addition Property
Adding on both sides of the equal sign
Subtraction Property
Subtracting on both sides of the equal sign
79 terms
Geometry Theorems, Postulates, and Definitions
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 real numbers in such…
If B is between A and C, then AB+ BC= AC
If in <QOA, Ray OP lies inside of the angle, ... <QOP=<QOA-<POA
If point B lies on the interior of angle AOC, then angle AOB+…
Postulate 1 (Ruler Postulate)
The points on a line can be paired with real numbers in such…
Postulate 2 (Segment Addition Postulate)
If B is 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
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
43 terms
Geometry Postulates, Theorems, and Definitions
postulate 2.1
postulate 2.2
postulate 2.3
postulate 2.4
through any two points, there is exactly one point
through any three points not on the same line, there is exact…
a line contains at least two points
a plane contains at least three points not on the same line... p…
postulate 2.1
through any two points, there is exactly one point
postulate 2.2
through any three points not on the same line, there is exact…
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 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
33 terms
Geometry Theorems, Postulates, Definitions
Through any two points...
If two distinct lines intersect,
If two distinct planes intersect,
Through any three noncollinear points...
there is exactly one line.
then they intersect in exactly one point.
then they intersect in exactly one line.
there is exactly one plane.
Through any two points...
there is exactly one line.
If two distinct lines intersect,
then they intersect in 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
72 terms
Geometry Definitions, Postulates, and Theorems
Congruent triangles
All pairs of corresponding parts are c…
Congruent polygons
All pairs of corresponding parts are c…
All pairs of corresponding parts are congruent
Congruent triangles
All pairs of corresponding parts are corresponding parts are…
Congruent polygons
Congruent triangles
All pairs of corresponding parts are congruent
All pairs of corresponding parts are c…
Congruent triangles
84 terms
Geometry- Postulates, Theorems, and Definitions
Addition Property
Subtraction Property
Multiplication Property
Division Property
if a=b and c=d, then a+c=b+d
if a=b and c=d, then a-c=b-d
if a=b then ca=cb
if a=b then a/c=b/c where c doesn't = 0
Addition Property
if a=b and c=d, then a+c=b+d
Subtraction Property
if a=b and c=d, then a-c=b-d
59 terms
Geometry Definitions Postulates and Theorems
Definition of Supplementary Angles
Definition of Alternate Interior Angles
Definition of Alternate Exterior angles
Definition of Corresponding Angles
2 angles whose measures have a sum of 180 degrees
2 non-adjacent angles that lie on opposite sides of the trans…
2 angles who are on opposite sides of the transversal and out…
2 angles who are on the same side of the transversal and the…
Definition of Supplementary Angles
2 angles whose measures have a sum of 180 degrees
Definition of Alternate Interior Angles
2 non-adjacent angles that lie on opposite sides of the trans…
72 terms
Geometry Theorems, Definitions, and postulates
Definitions
Complementary Angles
Supplementary angles
theorem
Definitions
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 degrees
a statement that can be proven
Definitions
Definitions
Complementary Angles
Two angles whose measures equal 90 degrees
99 terms
Geometry theorems,postulates,definitions
space
collinear points
coplanar points
intersection
the set of all points
points all in one line
points all in one plane
the set of points that are in both figures
space
the set of all points
collinear points
points all in one line
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
33 terms
Geometry Definitions, Theorems, and Postulates
Def. of Congruent
Def. of Midpoint
Def. of Segment bisector
Def. of Acute angle
If 2 segments, or angles equal each other they are congruent.
A point on a line segment that divides it into two equal parts.
A line, ray or segment which cuts another line segment into t…
An angle that is less than 90 degrees.
Def. of Congruent
If 2 segments, or angles equal each other they are congruent.
Def. of Midpoint
A point on a line segment that divides it into two equal parts.
16 terms
Geometry Postulates, Theorems, and Definitions
Addition Prop of =
Subtraction Prop of =
Multiplication Prop of =
Division Prop of =
If a=b and c=d then a+c=b+d
If a=b and c=d then a-c=b-d
if a=b then ca=cb
a=b and c≠0 then a/c=b/c
Addition Prop of =
If a=b and c=d then a+c=b+d
Subtraction Prop of =
If a=b and c=d then a-c=b-d
48 terms
Geometry Theorems, Definitions, and Postulates
Midpoint Theorem
Linear Pair Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
If M is the midpoint of ĀB, then ĀM~MB
If two angles form a linear pair, then they are supplementary
If two angles are supplementary to the same angle (or two con…
If two angles are complementary to the same angle (or two con…
Midpoint Theorem
If M is the midpoint of ĀB, then ĀM~MB
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
Geometry Theorems, Postulates, and Definitions
if a conditional statement is true, th…
If two angles are right angles, then t…
If two angles are straight angles, the…
If angles are supplementary to the sam…
if p, then q ⇔ if ~q, then ~p
all rt ∠s ≅
all st ∠s ≅
if supp to same ∠ → ≅
if a conditional statement is true, th…
if p, then q ⇔ if ~q, then ~p
If two angles are right angles, then t…
all rt ∠s ≅
58 terms
Geometry Postulates, Theorems, and Definitions
Definition
Postulate
Theorem
Line Segment
a list of properties an object must have
a basic assumption
a statement that has been proven true
two points on a line and all points that lie between them
Definition
a list of properties an object must have
Postulate
a basic assumption
72 terms
Geometry Theorems, Definitions, and postulates
Definitions
Complementary Angles
Supplementary angles
theorem
Definitions
Two angles whose measures equal 90 degrees
two angles whose measures equal 180 degrees
a statement that can be proven
Definitions
Definitions
Complementary Angles
Two angles whose measures equal 90 degrees
23 terms
GEOMETRY THEOREMS,DEFINITIONS,AND POSTULATES
segment addition postulate
definition of a midpoint
angle addition postulate
definition of a bisector
if B is between A and C then AB+BC=AC
a point that bisects/divides the segment into 2 congruent seg…
if S is in the interior of angle PQR then PQS+SQR=PQR
a ray that divides an angle into 2 congruent segments
segment addition postulate
if B is between A and C then AB+BC=AC
definition of a midpoint
a point that bisects/divides the segment into 2 congruent seg…
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…
175 terms
Geometry Definitions, 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: On line AB in a given plane, choose any…
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…
1 of 10