Study sets matching "chapter 2 geometry proofs"
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Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Inductive reasoning
Conjecture
Counterexample
Negation
reasoning that uses a # of specific examples to arrive at a co…
a concluding statement (sentence) reached using inductive reas…
false example or and example that shows a conjecture is not tr…
of a sentence has the opposite meaning and opposite truth valu…
Inductive reasoning
reasoning that uses a # of specific examples to arrive at a co…
Conjecture
a concluding statement (sentence) reached using inductive reas…
Midpoint Theorem
Segment Addition Postulate
Reflexive Property
Symmetric Property
if m is the midpoint of AB, then AM is congruent to MB
if b is between A and C, then AB+BC=AC
AB is congruent to AB; angle ABC is congruent to ABC (can be u…
if AB is congruent to CD, then CD is congruent to AB
Midpoint Theorem
if m is the midpoint of AB, then AM is congruent to MB
Segment Addition Postulate
if b is between A and C, then AB+BC=AC
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactly one line
Through any two lines, there is exactly one point of intersect…
If two planes intersect they intersect at exactly one line
Through any three nonlinear points there is exactly one plane
Postulate 1-1
Through any two points there is exactly one line
Postulate 1-2
Through any two lines, there is exactly one point of intersect…
congruent supplements theorem
definition of complementary angles
Vertical angles theorem
Congruent supplements theorem
If two angles are complementary to congruent angles, then the…
If two angles add up to 90 degrees, then they are complementary
Vertical angles are congruent
If two angles are supplementary to congruent angles, the the t…
congruent supplements theorem
If two angles are complementary to congruent angles, then the…
definition of complementary angles
If two angles add up to 90 degrees, then they are complementary
Theorem 2.1: Vertical Angles
Theorem 2.2: Congruent Supplements Theo…
Theorem 2.3: Congruent Complements Theo…
Theorem 2.4
vertical angles are congruent
if two angles are supplements of the same angle, then the two…
if two angles are complements of the same angle, then the two…
all right angles are congruent
Theorem 2.1: Vertical Angles
vertical angles are congruent
Theorem 2.2: Congruent Supplements Theo…
if two angles are supplements of the same angle, then the two…
Midpoint Theorem
Segment Addition Postulate
Reflexive Property
Symmetric Property
if m is the midpoint of AB, then AM is congruent to MB
if b is between A and C, then AB+BC=AC
AB is congruent to AB; angle ABC is congruent to ABC (can be u…
if AB is congruent to CD, then CD is congruent to AB
Midpoint Theorem
if m is the midpoint of AB, then AM is congruent to MB
Segment Addition Postulate
if b is between A and C, then AB+BC=AC
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
Conjecture
Inductive Reasoning
Counterexample
Deductive Reasoning
an educated guess based on known information
reasoning that uses a number of specific examples to arrive at…
specific case for which a conjecture is false
method using logic to draw conclusions based upon definitions,…
Conjecture
an educated guess based on known information
Inductive Reasoning
reasoning that uses a number of specific examples to arrive at…
Reflexive Property
Symmetric Property
communitive property
Transitive Property
any segment or angle is congruent to itself ... a=a
Swapping the equal sign. If 5+3=8, then 8=5+3
5+3=3+5
If a=b and b=c, then a=c
Reflexive Property
any segment or angle is congruent to itself ... a=a
Symmetric Property
Swapping the equal sign. If 5+3=8, then 8=5+3
Proof
What is the most important part of writ…
Addition Property of Equality
Subtraction Property of Equality
An argument that uses logic, definitions, properties, and prev…
Giving justification to show that every step is valid
If a = b, then a + c = b + c
If a = b, then a - c = b - c
Proof
An argument that uses logic, definitions, properties, and prev…
What is the most important part of writ…
Giving justification to show that every step is valid
Proof
Hypothesis
Conclusion
Converse
If/Then statement, with a hypothesis and conclusion. ... Ex: If…
"if" part of a proof... Ex: dog has a leash
"then" part of a proof... Ex: it has an owner
Statement opposite of proof statement. Can usually tell if a p…
Proof
If/Then statement, with a hypothesis and conclusion. ... Ex: If…
Hypothesis
"if" part of a proof... Ex: dog has a leash
Conditional statement
Conditional
Converse
Inverse
A statement that can be written in if-then form. ... (P then q)
If an angle is right, then it is 90 degrees
If an angle is right, then it is 90 degrees
If an angle is not 90 degrees, then it is not a right angle
Conditional statement
A statement that can be written in if-then form. ... (P then q)
Conditional
If an angle is right, then it is 90 degrees
Vertical angles congruence theorem
Congruent supplements theorem
Linear pair postulate
Right angle congruence theorem
Angle 1 is congruent to angle 2 and angle 2 is congruent to an…
If angle 1 and angle 2 are supplementray and angle 2 and angle…
If two angles form a linear pair (180 line), then they are sup…
All right angles are congruent
Vertical angles congruence theorem
Angle 1 is congruent to angle 2 and angle 2 is congruent to an…
Congruent supplements theorem
If angle 1 and angle 2 are supplementray and angle 2 and angle…
midpoint theorem
segment addition postulate
reflexive property
symmetric property
If m is the midpoint of line AB the line AM is congruent to li…
If B is between A and C then AB+BC=AC
line AB is congruent to AB
if line AB is congruent to line CD then line CD is congruent t…
midpoint theorem
If m is the midpoint of line AB the line AM is congruent to li…
segment addition postulate
If B is between A and C then AB+BC=AC
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 doesn't = 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
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactly one line
Through any two lines, there is exactly one point of intersect…
If two planes intersect they intersect at exactly one line
Through any three nonlinear points there is exactly one plane
Postulate 1-1
Through any two points there is exactly one line
Postulate 1-2
Through any two lines, there is exactly one point of intersect…
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a=b, then a+c=b+c... When you add something to both sides of a…
If a=b, then a-c=b-c... When you subtract something from both sid…
If a=b, then ac=bc... When you multiply both sides of an equation…
If a=b and c≠0, then a/c=b/c... When you divide both sides of an…
Addition Property of Equality
If a=b, then a+c=b+c... When you add something to both sides of a…
Subtraction Property of Equality
If a=b, then a-c=b-c... When you subtract something from both sid…
flowchart proof
paragraph proof
Common Segments Theorem
Vertical Angles Theorem
uses boxes and arrows to show the structure of the proff
presents the steps of a proof and their matching reasons as se…
vertical angles are congruent
flowchart proof
uses boxes and arrows to show the structure of the proff
paragraph proof
presents the steps of a proof and their matching reasons as se…
if-then statements
converse of a conditional
counterexample
biconditional
conditional statements
interchanges the hypothesis and the conclusion
words or diagram that prove an if-then statement is false
conditional and its converse are both true
if-then statements
conditional statements
converse of a conditional
interchanges the hypothesis and the conclusion
segment addition postulate
Definition of a midpoint
definition of segment bisector
definition of congruent segments
(P) IF B is between A and C, THEN AB+BC=AC
(D) IF P is the midpoint of segment AB THEN segment AP≅ segmen…
(D) line, segment, or ray that intersects the segment at its m…
(D) IF segment DE≅segment FG THEN DE=FG
segment addition postulate
(P) IF B is between A and C, THEN AB+BC=AC
Definition of a midpoint
(D) IF P is the midpoint of segment AB THEN segment AP≅ segmen…