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Study sets matching "geometry postulates theorems chapter 2"

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…
21 terms
Geometry Postulates and Theorems (Chapter 2)
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one p…
A line contains at least two points.
A plane contains at least three noncollinear points.
Postulate 2.1
Through any two points, there is exactly one line.
Postulate 2.2
Through any three noncollinear points, there is exactly one p…
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…
25 terms
Geometry Chapter 2 Postulates and Theorems
Through any two points, there is exact…
Through any three non-collinear points…
A line contains at least.........?
A plane contains at least.............…
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one p…
A line contains at least two points
A plane contains at least three non-collinear points
Through any two points, there is exact…
Through any two points, there is exactly one line.
Through any three non-collinear points…
Through any three noncollinear points, there is exactly one p…
29 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement, the statement that immediately fo…
A statement of the form "If A, then B." The part following if…
An educated guess.
The statement formed by negating both the hypothesis and conc…
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If A, then B." The part following if…
Geometry: Postulates & Theorems (Chapter 2)
(Theorem 2.1, Midpoint Theorem) If M i…
(Theorem 2.2, Angle Bisector Theorem)…
(Theorem 2.3) Vertical angles are...
(Theorem 2.4) If 2 lines are perpendic…
1/2 of AB
1/2 m<ABC
congruent
congruent adjacent angles
(Theorem 2.1, Midpoint Theorem) If M i…
1/2 of AB
(Theorem 2.2, Angle Bisector Theorem)…
1/2 m<ABC
25 terms
Geometry Chapter 2 Postulates and Theorems
Through any two points, there is exact…
Through any three non-collinear points…
A line contains at least.........?
A plane contains at least.............…
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one p…
A line contains at least two points
A plane contains at least three non-collinear points
Through any two points, there is exact…
Through any two points, there is exactly one line.
Through any three non-collinear points…
Through any three noncollinear points, there is exactly one p…
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
31 terms
Geometry Chapter 2 Postulates and Theorems
51 terms
Geometry Postulates, Theorems, and Definitions (Through Chapter 2)
If B is between A and C, then
If point D lies in the interior of ㄥAB…
If ㄥABC is a straight angle and D is a…
A line contains at least _____ points;…
AB + BC = AC
mㄥABD + mㄥCBD = mㄥABC
mㄥABD + mㄥCBD = 180॰
2, 3, 4
If B is between A and C, then
AB + BC = AC
If point D lies in the interior of ㄥAB…
mㄥABD + mㄥCBD = mㄥABC
25 terms
Geometry Chapter 2 Postulates and Theorems
Through any two points, there is exact…
Through any three non-collinear points…
A line contains at least.........?
A plane contains at least.............…
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one p…
A line contains at least two points
A plane contains at least three non-collinear points
Through any two points, there is exact…
Through any two points, there is exactly one line.
Through any three non-collinear points…
Through any three noncollinear points, there is exactly one p…
19 terms
Holt Geometry Definitions, Postulates, Theorems Chapter 2
definition of congruent segments
segment addition postulate
definition of congruent angles
angle addition postulate
two segments that have the same length
if b is between a and c, then ab+bc=ac
angles that have the same measure
if S is in the interior of angle PQR, then the measure of ang…
definition of congruent segments
two segments that have the same length
segment addition postulate
if b is between a and c, then ab+bc=ac
16 terms
Geometry - Chapter 2 - Triangles - Theorems & Postulates
Postulate 2.1 - SAS (Side-Angle-Side)
Postulate 2.2 - ASA (Angle-Side-Angle)
Post 2.3 SSS (Side-Side-Side)
CPCTC (DEFINITION)
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 three sides of one triangle are congruent to the correspon…
If two triangles are congruent, the six pairs of correspondin…
Postulate 2.1 - SAS (Side-Angle-Side)
If two sides and the included angle of one triangle are congr…
Postulate 2.2 - ASA (Angle-Side-Angle)
If two angles and the included side of one triangle are congr…
29 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement, the statement that immediately fo…
A statement of the form "If A, then B." The part following if…
An educated guess.
The statement formed by negating both the hypothesis and conc…
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If A, then B." The part following if…
8 terms
Honors Geometry - Chapter 2 Postulates & Theorems
Law of Detachment
Law of Syllogism
Properties of Congruence
Vertical Angles Theorem
If a conditional is true and its hypothesis is true, then its…
If p→q and q→r are true statements, then p→r is a true statem…
Reflexive Property: AB≅AB and ∠A≅∠A. Symmetric Property: If A…
Vertical angles are congruent.
Law of Detachment
If a conditional is true and its hypothesis is true, then its…
Law of Syllogism
If p→q and q→r are true statements, then p→r is a true statem…
53 terms
Geometry Chapter 2 Vocab, Theorems, Postulates
Line
Plane
Line Segment
Ray
an infinite set of points that extends in two directions
named using one capitol letter or using four points in the pl…
the line segment AB consists of the points A and B and all po…
the ray AB consists of the initial point A and all points on…
Line
an infinite set of points that extends in two directions
Plane
named using one capitol letter or using four points in the pl…
27 terms
Geometry Chapter 2 - Definitions, Theorems, and Postulates
If-Then/Conditional Statement
Hypothesis
Conclusion
Converse
A statement whose basic format is "If p, the q." There are mu…
"If" part of a conditional statement
"Then" part of a conditional statement
Formed by interchanging the hypothesis and conclusion of a co…
If-Then/Conditional Statement
A statement whose basic format is "If p, the q." There are mu…
Hypothesis
"If" part of a conditional statement
24 terms
Chapter 2 Geometry Postulates and Theorems
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through an two points, there is exactly one line
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
Postulate 2.1
Through an two points, there is exactly one line
Postulate 2.2
Through any three points not on the same line, there is exact…
32 terms
Geometry Chapter 2: postulates and theorems
2.1 Postulate
2.2 Postulate
2.3 Postulate
2.4 Postulate
through any two points there is one line
through any three noncollinear points there is one plane
one line has at least two points
one plane has at least three noncollinear points
2.1 Postulate
through any two points there is one line
2.2 Postulate
through any three noncollinear points there is one plane
9 terms
Geometry-Chapter 2 Postulates and Theorems
Postulate 2.1... Points and a line
Postulate 2.2... Three points and a plane
Postulate 2.3
Postulate 2.4
Through any two points, there is exactly one line
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
Postulate 2.1... Points and a line
Through any two points, there is exactly one line
Postulate 2.2... Three points and a plane
Through any three points not on the same line, there is exact…
16 terms
GEOMETRY CHAPTER 2 POSTULATES/THEOREMS
line 1
plane 1
line 2
plane 2
Through any two points, there is exactly one line
Through any three noncollinear points, there is exactly one p…
A line contains at least two points
A plane contains at least three noncollinear points
line 1
Through any two points, there is exactly one line
plane 1
Through any three noncollinear points, there is exactly one p…
14 terms
Geometry Chapter 2 Theorems and Postulates
Two point postulate
Line point postulate
Line intersection postulate
Three point postulate
Through any two points there is exactly one line
A line contains at least two points
If two lines intersect and then they intersect at exactly one…
Through any three noncollinear points there is exactly one pl…
Two point postulate
Through any two points there is exactly one line
Line point postulate
A line contains at least two points
17 terms
Geometry Postulates and Theorems Chapter 2
Segment Addition Postulate
Angle Addition Postulate
Midpoint Theorem
Angle Bisector Theorem
If B is between A and C, then AB + BC = AC
If point B lies on the interior of <AOC, then m<AOB + m<BOC =…
If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB
If BX is the bisector of <ABC, then m<ABX = 1/2m<ABC and m<XB…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If point B lies on the interior of <AOC, then m<AOB + m<BOC =…
15 terms
chapter 2 geometry postulates and theorems
reflexive
symmetric
transitive
midpoint theorem
a=a
a=b, b=a
if a =b, and b=c, then a=c
if m is the midpoint of AB, then Am = 1/2AB and MB =1/2 AB
reflexive
a=a
symmetric
a=b, b=a
37 terms
Geometry Postulates and Theorems Chapter 2
Inductive Reasoning
Conjecture
Conditional Statement
Hypothesis
reasoning based on patterns you observe
a conclusion you reach using inductive reasoning
an if-then statement
the part following the if
Inductive Reasoning
reasoning based on patterns you observe
Conjecture
a conclusion you reach using inductive reasoning
52 terms
Geometry Postulates, Theorems, and Definitions (Through Chapter 2)
If B is between A and C, then
If point D lies in the interior of ㄥAB…
If ㄥABC is a straight angle and D is a…
A line contains at least _____ points;…
AB + BC = AC
mㄥABD + mㄥCBD = mㄥABC
mㄥABD + mㄥCBD = 180॰
2, 3, 4
If B is between A and C, then
AB + BC = AC
If point D lies in the interior of ㄥAB…
mㄥABD + mㄥCBD = mㄥABC
34 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement, the statement that immediately fo…
A statement of the form "If A, then B." The part following if…
An educated guess.
The statement formed by negating both the hypothesis and conc…
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If A, then B." The part following if…
19 terms
Holt Geometry Definitions, Postulates, Theorems Chapter 2
definition of congruent segments
segment addition postulate
definition of congruent angles
angle addition postulate
two segments that have the same length
if b is between a and c, then ab+bc=ac
angles that have the same measure
if S is in the interior of angle PQR, then the measure of ang…
definition of congruent segments
two segments that have the same length
segment addition postulate
if b is between a and c, then ab+bc=ac
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…
15 terms
Geometry: Chapter 2-Postulates, Theorems, and Definitions
Definition of Congruence
Segment Addition Postulate
Angle Addition Postulate
Postulate 5
If line segment AB ≅ line segment CD, then AB = CD
If B is between A and C, then AB+BC=AC
If P is in the interior of ∠RST, then m∠RSP+m∠PST = m∠RST
Through any two points, there exists exactly one line.
Definition of Congruence
If line segment AB ≅ line segment CD, then AB = CD
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
24 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Contrapositive
Converse
In a conditional statement, the statement that immediately fo…
A statement of the form "If p, then q".
If ~ q then ~ p
If q then p
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If p, then q".
17 terms
Chapter 2 Math Theorems, Postulates and Definitions Geometry
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair of Angles
2 angles whose sum is always 90 degrees
2 angles whose sum is always 180 degrees
A pair of angles that share a common side, and have no common…
A pair of adjacent angles whose non-common sides form opposit…
Complementary Angles
2 angles whose sum is always 90 degrees
Supplementary Angles
2 angles whose sum is always 180 degrees
34 terms
Lovett Geometry Chapter 2 Postulates, Theorems and Definitions
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
On line AB in a given plane, chose any point O between A and…
If point B lies in the interior of angle AOC, then the measur…
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
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
17 terms
Honors Geometry Theorems & Postulates Chapter 2
Segment Addition Postulate
Angle Addition Postulate
Pythagorean Theorem
Linear Pair Theorem
If B is between A and C, then AB + BC = AC
If S is in the interior of angle PQR, then m<PQS + m<SQR = m<…
a2 + b2 = c2
If 2 angles form a linear pair, then they are supplementary
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If S is in the interior of angle PQR, then m<PQS + m<SQR = m<…
16 terms
Geometry: chapter 2 theorems/definitions/postulates/concepts
If segments, rays or lines meet to for…
If two angles sum to 90° (or form a ri…
If two angles sum to 180° (or form a s…
If two angles are complementary to the…
Then they are perpendicular ... (Definition)
Then they are complementary ... (Definition)
Then they are supplementary... (Definition)
Then they are congruent ... (Theorem)
If segments, rays or lines meet to for…
Then they are perpendicular ... (Definition)
If two angles sum to 90° (or form a ri…
Then they are complementary ... (Definition)
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
17 terms
geometry chapter 2: postulated and theorems
contrapositive
conjecture
distributive property
theorem
if ~q, then ~p
conclusion from inductive reasoning
a(b+c)= ab+ac
statement you prove
contrapositive
if ~q, then ~p
conjecture
conclusion from inductive reasoning
8 terms
Geometry Chapter 2 Properties, Postulates, and Theorems
a=a
If a=b, then b=a
If a=b and b=c, then a=c
All right angles are congruent
Reflexive Property (=)
Symmetric Property (=)
Transitive Property (=)
Right Angles Congruence Theorem
a=a
Reflexive Property (=)
If a=b, then b=a
Symmetric Property (=)
57 terms
Geometry Honors - Chapter 2 Theorems/Postulates/Definitions
Inductive Reasoning
Conjecture
Counterexample
Statement
logic used to reach a conclusion or conjecture
A conclusion that is maybe true or false
example that shows that a conjecture is false
a sentence that can be either True or False
Inductive Reasoning
logic used to reach a conclusion or conjecture
Conjecture
A conclusion that is maybe true or false
8 terms
Geometry Chapter 2 Theorems, Properties, Definitions, and Postulates.
Reflexive Property Of Equality
Transitive Property Of Equality
Symmetric Property Of Equality
Linear Pair Theorem
A=A.
If a = b, and b = c, then a = c.
If a = b, then b = a.
If two angles form a linear pair, then they are supplementary.
Reflexive Property Of Equality
A=A.
Transitive Property Of Equality
If a = b, and b = c, then a = c.
12 terms
Geometry Postulates, Definitions, and Theorems chapter 2
definition of midpoint
biconditional
angle bisector theorem
midpoint theorem
a line/ point divides a segment into two congruent segments
Both the conditional statement and the converse statement are…
If line BX is the bisector of angle ABC, then the measure of…
If M is midpoint of segment AB, then AM= 1/2 AB, and MB= 1/2 AB
definition of midpoint
a line/ point divides a segment into two congruent segments
biconditional
Both the conditional statement and the converse statement are…
29 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement, the statement that immediately fo…
A statement of the form "If A, then B." The part following if…
An educated guess.
The statement formed by negating both the hypothesis and conc…
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If A, then B." The part following if…
33 terms
Geometry Chapter 2 terms/postulates/theorems
conditional statement
converse
inverse
contrapositive
a statement that can be written in the form if p, then q... ex:…
is formed by exchanging the hypothesis and conclusion of the…
formed by negating both the hypothesis and conclusion of the…
formed by negating both the hypothesis and the conclusion of…
conditional statement
a statement that can be written in the form if p, then q... ex:…
converse
is formed by exchanging the hypothesis and conclusion of the…
29 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement, the statement that immediately fo…
A statement of the form "If A, then B." The part following if…
An educated guess.
The statement formed by negating both the hypothesis and conc…
Conclusion
In a conditional statement, the statement that immediately fo…
Conditional Statement
A statement of the form "If A, then B." The part following if…
16 terms
Geometry Chapter 2: Theorems, Postulates, and Definitions
addition property
subtraction property
multiplication property
division property
3x - 5 = 10... +5 +5
3x + 5 = 10... -5 -5
c/4 = 12... x4 x4
10x = 50... ___ ___... 10 10
addition property
3x - 5 = 10... +5 +5
subtraction property
3x + 5 = 10... -5 -5
31 terms
Holt Geometry Definitions, Postulates, Theorems Chapter 2
definition of congruent segments
segment addition postulate
definition of congruent angles
angle addition postulate
two segments that have the same length
if b is between a and c, then ab+bc=ac
angles that have the same measure
if S is in the interior of angle PQR, then the measure of ang…
definition of congruent segments
two segments that have the same length
segment addition postulate
if b is between a and c, then ab+bc=ac
16 terms
Geometry Chapter 2: Definitions, Postulates, and Theorems Review
Angle Bisector
Complementary Angles
Congruent Angles
Congruent Segments
A ray that divides an angle into two congruent angles
Two angles whose measures have a sum of 90°
Angles that have the same measure
Two segments that have the same measure
Angle Bisector
A ray that divides an angle into two congruent angles
Complementary Angles
Two angles whose measures have a sum of 90°
13 terms
Chapter 2 Geometry: Theorems, Postulates, and Definitions
Conjecture
^
~
An educated guess
and
or
negation
Conjecture
An educated guess
^
and
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