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Study sets matching "postulates geometry theorems laws"

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Study sets matching "postulates geometry theorems laws"

26 terms
Geometry Laws, Theorems, and Postulates
Law of Detatchment
Law of Syllogism
Postulate 1.1
Postulate 1.2
If p --> q is a true statement, and p is true, then q is true.
If p --> q, and q --> r, then p --> r.
Through any 2 points there exists exactly one line
If 2 distinct lines intersect, then they intersect in exactly…
Law of Detatchment
If p --> q is a true statement, and p is true, then q is true.
Law of Syllogism
If p --> q, and q --> r, then p --> r.
26 terms
Geometry Laws, Theorems, and Postulates
Law of Detatchment
Law of Syllogism
Postulate 1.1
Postulate 1.2
If p --> q is a true statement, and p is true, then q is true.
If p --> q, and q --> r, then p --> r.
Through any 2 points there exists exactly one line
If 2 distinct lines intersect, then they intersect in exactly…
Law of Detatchment
If p --> q is a true statement, and p is true, then q is true.
Law of Syllogism
If p --> q, and q --> r, then p --> r.
114 terms
Geometry Postulates, Theorems, Laws
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…
94 terms
Geometry postulates, laws, and theorems
Segment addition postulate
Angle addition postulate
Linear pair postulate
Area addition postulate
If 3 pt. Are Collinear Ab+Bc=ac
Angle AOB+BOC=AOC
If two angles form a linear pair, then they are supplementary
The area of a region is the su. Of the areas of its nonoverla…
Segment addition postulate
If 3 pt. Are Collinear Ab+Bc=ac
Angle addition postulate
Angle AOB+BOC=AOC
127 terms
Geometry Postulates, Theorems, Laws, and Formulas
Ruler Postulate
Segment Addition Postulate
Distance Formula
Protractor Postulate
The points on a line can be matched one to one with real numb…
If B is between A and C, then AB+BC=AC
The distance between A(x₁,y₁) and B(x₂,y₂) =√(x₂-x₁)+(y₂-y₁)
If point O is the center of a circle and points A and B are o…
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
47 terms
Geometry Postulates, Laws, Properties, Theorems
Through any 2 points,
If 2 distinct lines intersect,
If 2 planes intersect,
Through any 3 non-collinear points,
there is exactly one line
then they intersect in exactly one point
then they intersect at exactly one line
there is exactly one plane
Through any 2 points,
there is exactly one line
If 2 distinct lines intersect,
then they intersect in exactly one point
45 terms
Geometry Laws, Properties, Theorems, and Postulates
Law of Detachment
Law of Syllogism
Segment Addition Postulate
Angle Addition Postulate
If p -> q is true and p is true, then q is true
If p -> q and q -> r, then p -> r
If points A, B, and C are collinear and B is between A and C,…
If point T is interior of ∠AXC, then m∠AXT + m∠TXC = m∠AXC
Law of Detachment
If p -> q is true and p is true, then q is true
Law of Syllogism
If p -> q and q -> r, then p -> r
36 terms
Geometry (Postulates, Formulas, Laws, Properties, Theorems, and Slopes)
1-1
1-2
1-3
1-4
Through any two points there in exactly one line
Two distinct lines intersect in exactly one point
If two distinct planes intersect, then they intersect in exac…
Through any non-collinear points, there is exactly one plane
1-1
Through any two points there in exactly one line
1-2
Two distinct lines intersect in exactly one point
64 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
12 terms
Geometry Chapter 2 (Theorems, Laws, Postulates and vocab)
All right angles are congruent
If <1 and <2 are supplementary and <3…
If <4 and <5 are complementary and <6…
vertical angles are congruent
right angles congruence theorem
Congruent Supplements Theorem
Congruent Complements Theorem
vertical angles congruence theorem
All right angles are congruent
right angles congruence theorem
If <1 and <2 are supplementary and <3…
Congruent Supplements Theorem
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
64 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
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.
64 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
36 terms
Geometry (Postulates, Formulas, Laws, Properties, Theorems, and Slopes)
1-1
1-2
1-3
1-4
Through any two points there in exactly one line
Two distinct lines intersect in exactly one point
If two distinct planes intersect, then they intersect in exac…
Through any non-collinear points, there is exactly one plane
1-1
Through any two points there in exactly one line
1-2
Two distinct lines intersect in exactly one point
19 terms
Geometry Honors Theorems & Postulates
Right Angle Congruence Theorem
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
If 2 angles are right angles, then they are congruent
If 2 angles are vertical angles, then they are congruent
If 2 angles are supplementary to the same angle or congruent…
If 2 angles are complementary to the same angle or congruent…
Right Angle Congruence Theorem
If 2 angles are right angles, then they are congruent
Vertical Angles Theorem
If 2 angles are vertical angles, then they are congruent
24 terms
Honors Geometry Postulates, Properties, Theorems, & Laws.
law of detachment
law of syllogism
postulate 5
postulate 6
if P implies Q is a true conditional statement and P is true,…
if P implies Q and Q implies R is true, then P implies R.
through any two points there exists exactly one line.
a line contains at least two points.
law of detachment
if P implies Q is a true conditional statement and P is true,…
law of syllogism
if P implies Q and Q implies R is true, then P implies R.
27 terms
geometry: postulates, properties, statements, laws and theorems
segment addition postulate
law of detachment
conditional statement
hypothesis
if SRT are collinear and R is between S and T then SR + RT= ST
if the hypothesis of a conditional statement is true then the…
a statement in the form of if______then______
"if" portion of a conditional statement
segment addition postulate
if SRT are collinear and R is between S and T then SR + RT= ST
law of detachment
if the hypothesis of a conditional statement is true then the…
80 terms
Adv. Geometry-Laws, Properties, Postulates, Theorems, Corollaries
Unique Line Postulate
Intersecting Lines Postulate
Intersecting Planes Postulate
Plane Postulate
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 nonlinear points there is exactly one plane
Unique Line Postulate
Through any two points there is exactly one line
Intersecting Lines Postulate
If two lines intersect, then they intersect in exactly one po…
6 terms
Geometry Postulates & Theorems
Corresponding Angles Converse
Alternate Interior Angles Converse
Alternative Exterior Angles Converse
Consecutive Interior Angles converse
If two lines are cut by a transversal so the corresponding an…
If two lines are cut by a transversal so the alternate interi…
if two lines are cut by a transversal so the alternate exteri…
If two lines are cut by a transversal so the consecutive inte…
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding an…
Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interi…
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°
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…
18 terms
Geometry Proofs Postulates and Laws Properties and Theorems
Law of detachment
Law of Syllogism
Reflexive Property
Symmetric Property
if p implies q is a true conditional statement and p is true…
if p implies q and q imply r are true conditional statements…
for any real number a, a=a
if a=b then b=a
Law of detachment
if p implies q is a true conditional statement and p is true…
Law of Syllogism
if p implies q and q imply r are true conditional statements…
16 terms
Important Geometry Theorems/Postulates
If two congruent angles form a linear…
If two angles are vertical angles, the…
If there is a line and a point not on…
If there exists a line and a point, th…
If two congruent angles form a linear…
If two angles are vertical angles, the…
12 terms
Geometry - Postulates and theorems
segment addition postulate
reflexive property
congruent
midpoint theorem
AB + BC = AC
any segment or angle is congruent/equal to itself (AB = AB) (…
have equal measure
If AB + BC = AC and AB=BC
segment addition postulate
AB + BC = AC
reflexive property
any segment or angle is congruent/equal to itself (AB = AB) (…
67 terms
geometry--midterm postulates, theorem, properties, and laws
The distance between two points is the…
If A, B, and C are collinear and B is…
If B is on the interior of ∠ADC, then…
Any line segment will have exactly one…
ruler postulate
segment addition postulate
angle addition postulate
midpoint postulate
The distance between two points is the…
ruler postulate
If A, B, and C are collinear and B is…
segment addition postulate
16 terms
Geometry Postulates and Theorems
corresponding angles
congruent corresponding angles
SSS Postulate
SAS Postulate
If two parallel lines are cut by a transversal, then correspo…
If two lines are cut by a transversal and corresponding angle…
If three sides of one triangle are congruent to three sides o…
If two sides and the included angle of one triangle are congr…
corresponding angles
If two parallel lines are cut by a transversal, then correspo…
congruent corresponding angles
If two lines are cut by a transversal and corresponding angle…
12 terms
Geometry Postulates/ Theorems
Perpendicular Bisector Theorem
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Same-Side Interior Angles Postulate
If a point is on the perpendicular bisector of a segment, the…
If two parallel lines are cut by a transversal, then the pair…
If two parallels are cut by a transversal, then the pair of a…
If two parallel lines are cut by a transversal, then the pair…
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, the…
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pair…
17 terms
Postulates and Theorems of Geometry 3
Corresponding Angles Postulate (3-1)
Alternate Interior Angles Theorem (3-1)
Consecutive Interior Angles Theorem (3…
Alternate Exterior Angles Theorem (3-3)
If two parallel lines are cut by a transversal, the correspon…
If two parallel lines are cut by a transversal, the alternate…
If two parallel lines are cut by a transversal, the consecuti…
If two parallel lines are cut by a transversal, the alternate…
Corresponding Angles Postulate (3-1)
If two parallel lines are cut by a transversal, the correspon…
Alternate Interior Angles Theorem (3-1)
If two parallel lines are cut by a transversal, the alternate…
18 terms
Geometry Postulates and 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 between A and C, then AB + BC = AC.
Given line AB and a point O on line AB, all rays that can be…
If B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC.
Ruler Postulate
The points on a line can be paired with the real numbers in s…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
18 terms
Geometry- Theorems and Postulates
Postulate
Theorem
Intersection of 2 lines is exactly...
Intersection of 2 planes is exactly...
Statement accepted without proof
Conjecture (mathematical hypothesis) that has been proved
1 point
1 line
Postulate
Statement accepted without proof
Theorem
Conjecture (mathematical hypothesis) that has been proved
67 terms
geometry--midterm postulates, theorem, properties, and laws
The distance between two points is the…
If A, B, and C are collinear and B is…
If B is on the interior of ∠ADC, then…
Any line segment will have exactly one…
ruler postulate
segment addition postulate
angle addition postulate
midpoint postulate
The distance between two points is the…
ruler postulate
If A, B, and C are collinear and B is…
segment addition postulate
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°
31 terms
Geometry Theorems, Postulates, and Properties
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.
The measure of ∠AOB, which can be written as m∠AOB, is equal…
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, 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
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
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
6 terms
Geometry Chapter 3 - Theorems and Postulates
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Theorem
Alternate Interior Angles Theorem
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 parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
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…
15 terms
Geometry Postulates and Theorems Chapter 3
Postulate 3-1 Same-side Interior Angle…
Theorem 3-1 Alternate Interior Angles…
Theorem 3-2 Corresponding Angles Theor…
Theorem 3-3 Alternate Exterior Angles…
supplementary... m∠1 + m∠2 = 180
congruent
corresponding
exterior
Postulate 3-1 Same-side Interior Angle…
supplementary... m∠1 + m∠2 = 180
Theorem 3-1 Alternate Interior Angles…
congruent
19 terms
Geometry Vocab for the postulates and theorems
parallel pos.
perpendicular pos.
paragraph proof
transitive property of parallel lines
if there is a line and a point not on that line then there is…
if there is a line and a point not on that line then there is…
a proof written as a paragraph
if two lines are parallel to the same line then they are para…
parallel pos.
if there is a line and a point not on that line then there is…
perpendicular pos.
if there is a line and a point not on that line then there is…
27 terms
Geometry Theorems/Postulates
(2-4)Definition of midpoint:
(3-9)Definition of bisector:
(5-2)CPCF Theorem (segment):
(2-4)Definition of a circle:
If a point is the midpoint of a segment, it divides the segme…
If a figure is the the bisector of a segment, it divides the…
If figures are congruent, then corresponding segments are con…
If a figure is a circle, then its radii are congruent. (2-4)
(2-4)Definition of midpoint:
If a point is the midpoint of a segment, it divides the segme…
(3-9)Definition of bisector:
If a figure is the the bisector of a segment, it divides the…
64 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
30 terms
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 =…
83 terms
Geometry Postulates, Theorems, and Vocabulary
Postulate - 2.1
Postulate - 2.2
Postulate - 2.3
Postulate - 2.4
Through any two points, there 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
Postulate - 2.1
Through any two points, there is exactly one line
Postulate - 2.2
Through any three non collinear points, there is exactly one…
35 terms
Geometry Theorems and Postulates
If there are two points,
If there is a line,
Two points determine a ____
If there are three noncollinear points,
there is exactly one line that contains them.
then there are at least two points on the line
line
there is exactly one plane that contains them
If there are two points,
there is exactly one line that contains them.
If there is a line,
then there are at least two points on the line
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…
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.
61 terms
Geometry Theorems/Postulates
Same side interior angles postulate
Same side exterior angles postulate
Alternate Interior Angles Theorem
Corresponding Angles Theorem
If a transversal intersects two parallel lines, then same-sid…
If a transversal intersects two parallel lines, then same-sid…
If t intersects two parallel lines, then alternate interior a…
If t intersects two parallel lines, then corresponding angles…
Same side interior angles postulate
If a transversal intersects two parallel lines, then same-sid…
Same side exterior angles postulate
If a transversal intersects two parallel lines, then same-sid…
46 terms
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
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
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