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Study sets matching "geometry postulates theorems"

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
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
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
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…
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…
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) (…
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…
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…
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
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
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°
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…
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
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
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
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.
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…
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…
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…
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 =…
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
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…
58 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.
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
29 terms
Geometry Postulates and Theorems
Postulates points, planes, and lines
Postulates- intersection of planes and…
Ruler Postulate
Segment Addition Postulate
1.) Through any two pointd there is exactly one line.... 2.) Thr…
4.) If two lines intersect, then they intersect at one point.…
Points on a line can b put to a one to one correspondence wit…
If a point is in between two points then the distance from fi…
Postulates points, planes, and lines
1.) Through any two pointd there is exactly one line.... 2.) Thr…
Postulates- intersection of planes and…
4.) If two lines intersect, then they intersect at one point.…
17 terms
Geometry Theorems and Postulates
Triangle Sum Theorem
Exterior Angle Theorem
Exterior Angle Inequality Theorem
Triangle Inequality Theorem
the sum of the measures of the interior angles of a triangle…
the measure of an exterior angle of a triangle is equal to th…
the measure of an exterior angle of a triangle is greater tha…
the sum of the lengths of any 2 sides of a triangle is greate…
Triangle Sum Theorem
the sum of the measures of the interior angles of a triangle…
Exterior Angle Theorem
the measure of an exterior angle of a triangle is equal to th…
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
48 terms
Geometry Theorems and Postulates
Ruler Postulate
Segment Addition Postulate
Midpoint Formula
Distance Formula
Distance between points A and B (AB) is the absolute value of…
If B is between A and C, then AB+BC=AC. If AB+BC+AC, then B i…
If A (x1,y1) and B(x2,y2) are points in a coordinate plane, t…
If A (x1,y1) and B (x2,y2) are points in a coordinate plane,…
Ruler Postulate
Distance between points A and B (AB) is the absolute value of…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC. If AB+BC+AC, then B i…
19 terms
Geometry postulates and theorems
parallel lines
skew lines
parallel planes
transversal
Two lines that are coplanar and do NOT intersect.
Lines that do NOT intersect and are NOT coplanar.
Two planes that do NOT intersect.
A line that intersects two or more coplanar lines at differen…
parallel lines
Two lines that are coplanar and do NOT intersect.
skew lines
Lines that do NOT intersect and are NOT coplanar.
14 terms
Geometry: Postulates and Theorems
Postulate 1
Postulate 4
Postulate 5
Postulate 6
(Segment Addition Postulate)... if B is between A and C, then AB…
(Angle Addition Postulate)... if B lies in the interior of <AOC,…
a LINE contains at least 2 POINTS... a PLANE contains at least 3…
through any 2 POINTS there is exactly 1 LINE
Postulate 1
(Segment Addition Postulate)... if B is between A and C, then AB…
Postulate 4
(Angle Addition Postulate)... if B lies in the interior of <AOC,…
42 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement (if-then statement), the statement…
A statement written in an if then form... A statement of the for…
An educated guess based on known information... pg 78
The statement formed by negating both the hypothesis(educated…
Conclusion
In a conditional statement (if-then statement), the statement…
Conditional Statement
A statement written in an if then form... A statement of the for…
9 terms
Geometry Theorems/Postulates
AAA Similarity Polstulate
SAS Similarity Theorem
SSS Similarity Theorem
Triangle Proportionality Theorem
If two angles of one triangle are congruent to two angles of…
If an angle of one triangle is congruent to an angle of anthe…
If the corresponding sides of two triangles are in proportion…
If a line parallel to a side of a triangle intersects the oth…
AAA Similarity Polstulate
If two angles of one triangle are congruent to two angles of…
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of anthe…
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
22 terms
Geometry Postulates and Theorems
Postulate
Conjecture
Truth Value
Conditional Statement
A statement that doesn't have to be proven and is always true.
Idea based on observation.
Conditional statements truth value of either false or true.
Statement that is written in the form of:... "If p, then q."... "p"…
Postulate
A statement that doesn't have to be proven and is always true.
Conjecture
Idea based on observation.
170 terms
Geometry Postulates and Theorems
Any segment or angle is congruent to i…
If there exists a correspondence betwe…
If there exists a correspondence betwe…
If there exists a correspondence betwe…
Reflexive Property
Side-Side-Side Congruence (SSS)
Side-Angle-Side Congruence (SAS)
Angle-Side-Angle Congruence (ASA)
Any segment or angle is congruent to i…
Reflexive Property
If there exists a correspondence betwe…
Side-Side-Side Congruence (SSS)
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
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
Congruent Supplements Theorem
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 they…
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
Congruent Supplements Theorem
If two angles are supplementary to the same angle, then they…
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
43 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
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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