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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

Conditional Statement

If-then Form

Hypothesis

Conclusion

A logical statement that has two parts, a hypothesis and a co…

The form of a conditional statement that uses the words "if"…

The "if" part of a conditional statement written in if-then f…

The "then" part of a conditional statement written in if-then…

Conditional Statement

A logical statement that has two parts, a hypothesis and a co…

If-then Form

The form of a conditional statement that uses the words "if"…

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 intersec…

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 intersec…

Conjecture

Inductive Reasoning

Counterexample

Deductive Reasoning

an educated guess based on known information

reasoning that uses a number of specific examples to arrive a…

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 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

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…

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

Line postulate

Segment Addition postulate

Angle Addition postulate

Reflexive POE

Between any 2 points there's a line

If Q is between P and R, then PQ + QR = PR

If ray DF is in the interior of angle CDE, then the measure o…

a=a

Line postulate

Between any 2 points there's a line

Segment Addition postulate

If Q is between P and R, then PQ + QR = PR

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 s…

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 s…

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…

Proof

If/Then statement, with a hypothesis and conclusion. ... Ex: If…

Hypothesis

"if" part of a proof... Ex: dog has a leash

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 a…

If angle 1 and angle 2 are supplementray and angle 2 and angl…

If two angles form a linear pair (180 line), then they are su…

All right angles are congruent

Vertical angles congruence theorem

Angle 1 is congruent to angle 2 and angle 2 is congruent to a…

Congruent supplements theorem

If angle 1 and angle 2 are supplementray and angle 2 and angl…

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 intersec…

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 intersec…

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…

If a=b, then a-c=b-c... When you subtract something from both si…

If a=b, then ac=bc... When you multiply both sides of an equatio…

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…

Subtraction Property of Equality

If a=b, then a-c=b-c... When you subtract something from both si…

Conditional Statement

If-then Form

Hypothesis

Conclusion

A logical statement that has two parts, a hypothesis and a co…

The form of a conditional statement that uses the words "if"…

The "if" part of a conditional statement written in if-then f…

The "then" part of a conditional statement written in if-then…

Conditional Statement

A logical statement that has two parts, a hypothesis and a co…

If-then Form

The form of a conditional statement that uses the words "if"…

Commutative

Associative

Identity

Inverse

Addition: a plus b equals b plus a... Mult: a times b equals b t…

Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…

Add: a plus 0 equals a... Mult: a times 1 equals a

Add: A plus negative a equals zero... Mult: a times 1/a equals 1

Commutative

Addition: a plus b equals b plus a... Mult: a times b equals b t…

Associative

Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…

Perpendicular Lines

Biconditional Statement

Two Point Postulate

Line-Point Postulate

Lines that intersect to form right angles.

A statement that contains the phrase "if and only it".

Through any two points, there exists exactly one line.

A line contains at least two points.

Perpendicular Lines

Lines that intersect to form right angles.

Biconditional Statement

A statement that contains the phrase "if and only it".

Converse

Negation

Inverse

Contrapositive

Formed by switching the hypothesis and conclusion of a condit…

Is the denial of a statement (add the word "not"). A statemen…

Formed by negating both the hypothesis and conclusion of a co…

Formed by negating and switching the hypothesis and conclusio…

Converse

Formed by switching the hypothesis and conclusion of a condit…

Negation

Is the denial of a statement (add the word "not"). A statemen…

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 a(c)=b(c)

if a=b and c DOES NOT =, 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

Biconditional Statement

Conclusion

Conditional statement

Conjecture

A statement that can be written in the fom "p iff q"

The "then" part of a conditional statement

A statement that can be written as "if p then q" where p is t…

A statemnet that is believed to be true

Biconditional Statement

A statement that can be written in the fom "p iff q"

Conclusion

The "then" part of a conditional statement

Congruent Segments

Congruent Angles

Midpoint

Angle Bisector

line segments that have the same length.

angles with the same measure

the point that divides the segment into two congruent segments

a ray that divides the angle into two congruent segments

Congruent Segments

line segments that have the same length.

Congruent Angles

angles with the same measure

Congruent Segments

Congruent Angles

Midpoint

Angle Bisector

line segments that have the same length.

angles with the same measure

the point that divides the segment into two congruent segments

a ray that divides the angle into two congruent segments

Congruent Segments

line segments that have the same length.

Congruent Angles

angles with the same measure

proof

addition property of equality

subtraction property of equality

multiplication property of equality

an argument that uses logic, definition, properties/ postulat…

if A = B, then A+C = B+C

if A = B, then A-C = B-C

if A = B, then A**C = B**C

proof

an argument that uses logic, definition, properties/ postulat…

addition property of equality

if A = B, then A+C = B+C

conjecture

implications

statement

vertical angle Th

a conclusion you reach using inductive reasoning; educated gu…

Original:p--->q... Converse: q--->p... Inverse: ~p--->~q... Contraposi…

a sentence that's either true or false

vertical angles are congruent

conjecture

a conclusion you reach using inductive reasoning; educated gu…

implications

Original:p--->q... Converse: q--->p... Inverse: ~p--->~q... Contraposi…

Conditional Statement

If-then Form

Hypothesis

Conclusion

A logical statement that has two parts, a hypothesis and a co…

The form of a conditional statement that uses the words "if"…

The "if" part of a conditional statement written in if-then f…

The "then" part of a conditional statement written in if-then…

Conditional Statement

A logical statement that has two parts, a hypothesis and a co…

If-then Form

The form of a conditional statement that uses the words "if"…

Given, to prove, figure, statements, r…

Given, figure, previous statements

Congruent

Congruent segments

5 parts to a deductive proof

Three sources of statements

Two objects that have the same size and shape

Segments that have equal lengths

Given, to prove, figure, statements, r…

5 parts to a deductive proof

Given, figure, previous statements

Three sources of statements

Segment addition postulate

Angle addition postulate

Addition property of equality

Subtraction property of =

If B is between A and C, then AB + BC=AC

If p is in the interior of <RST, then the measure of <RST = <…

If a=b, then a+c=b+c

If a=b then a-c=b-c

Segment addition postulate

If B is between A and C, then AB + BC=AC

Angle addition postulate

If p is in the interior of <RST, then the measure of <RST = <…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The point on a line can be put into a one to one corresponden…

If B is between A and C, then AB + BC = AC.

Given ↔AB and a point O on ↔AB, all rays that can be drawn fr…

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR.

Ruler Postulate

The point on a line can be put into a one to one corresponden…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC.

Conditional Statement

If-then Form

Hypothesis

Conclusion

A logical statement that has two parts, a hypothesis and a co…

The form of a conditional statement that uses the words "if"…

The "if" part of a conditional statement written in if-then f…

The "then" part of a conditional statement written in if-then…

Conditional Statement

A logical statement that has two parts, a hypothesis and a co…

If-then Form

The form of a conditional statement that uses the words "if"…

Converse

Inverse

Contrapositive

Biconditional Statement

Exchange the hypothesis and the conclusion... p=>q / q=>p

Negate the hypothesis and conclusion of the conditional... p=>q…

first write the converse, then negate the hypothesis and the…

contains the phrase "if and only if". Can be read forwards an…

Converse

Exchange the hypothesis and the conclusion... p=>q / q=>p

Inverse

Negate the hypothesis and conclusion of the conditional... p=>q…

inductive reasoning

counterexample

law of detachment

law of syllogism

examining several specific situations to a mile at a conjecture

proves that a conjecture is false (just one is needed)

if p->q is true, then p is true and q is true

if p->q and q->r are true then p->r is also true (conclusion…

inductive reasoning

examining several specific situations to a mile at a conjecture

counterexample

proves that a conjecture is false (just one is needed)

AAP

def. of angle bisector

SAP

Def. of midpoint

Given: Picture... measure or angle 1 + measure of angle 2= measu…

Given:Ray BX bisects angle ABC... Conclusion: measure or angle 1…

G: B is the midpoint of AC̅̅̅̅... C: AB = BC (AB̅̅̅̅ ≅ BC̅̅̅̅)

AAP

Given: Picture... measure or angle 1 + measure of angle 2= measu…

def. of angle bisector

Given:Ray BX bisects angle ABC... Conclusion: measure or angle 1…

biconditional

conclusion

conditional

conjecture

a statement that is the combination of a conditional statemen…

the part of an if-then statement (conditional) that follows t…

an if-then statement

a conclusion reached by using inductive reasoning

biconditional

a statement that is the combination of a conditional statemen…

conclusion

the part of an if-then statement (conditional) that follows t…

congruent segments

congruent angles

right angle

linear pair

If segments are congruent, then they have the same measure.

If angles are congruent, then they have the same measure.

If an angle has a measure of 90 degrees, then it is a right a…

If angles are adjacent angles and are formed by opposite rays…

congruent segments

If segments are congruent, then they have the same measure.

congruent angles

If angles are congruent, then they have the same measure.

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

symmetric property (of congruence)

reflexive property (of congruence)

transitive property (of congruence)

segment addition postulate

if a=b then b=a

of a=a then a=a

of a=b and b=c then a=c

if b is between a and c, then ab + bc= ac

symmetric property (of congruence)

if a=b then b=a

reflexive property (of congruence)

of a=a then a=a

conjecture

inductive reasoning

counterexample

conditional statement

an unproven statement that is based on observations

used when you find a pattern and then write a conjecture

a specific case when a conjecture is false

a logical statement that has 2 parts: a hypothesis and a conc…

conjecture

an unproven statement that is based on observations

inductive reasoning

used when you find a pattern and then write a conjecture

Law of Detachment

Law of Syllogism

Vertical Angles Theorem

Congruent Supplements Theorem

if p --> q is true and p is true, them q is true. If the hypo…

if p --> q is true and q --> r is true, then p --> r is true

Vertical angles are congruent

If two angles are supplements of the same angle, then the two…

Law of Detachment

if p --> q is true and p is true, them q is true. If the hypo…

Law of Syllogism

if p --> q is true and q --> r is true, then p --> r is true

an if-then statement is a...

the "P" in a conditional (if-then) sta…

the "Q" in a conditional (if-then) sta…

a logical statement that has two parts…

conditional

hypothesis

conclusion

conditional statement

an if-then statement is a...

conditional

the "P" in a conditional (if-then) sta…

hypothesis

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 does not = 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

inductive reasoning

conjecture

statement

truth value

making a conclusion based on patterns and observations

a concluding statement reached using inductive reasoning

a sentence that is either true or false, represented using le…

whether a statement is true or false

inductive reasoning

making a conclusion based on patterns and observations

conjecture

a concluding statement reached using inductive reasoning

inductive reasoning

conjecture

counterexample

figural numbers

reasoning that uses a number of specific examples to arrive a…

a concluding statement reached using inductive reasoning

a false example

numbers that can be represented by evenly spaced points arran…

inductive reasoning

reasoning that uses a number of specific examples to arrive a…

conjecture

a concluding statement reached using inductive reasoning

conditional statements

converse statements

inverse statements

contrapositive statements

a logical if-then statement

switch the hypothesis and conclusion of a conditional statement

negate the hypothesis and conclusion of the original conditio…

switch and negate the hypothesis and conclusion of the origin…

conditional statements

a logical if-then statement

converse statements

switch the hypothesis and conclusion of a conditional statement

Conjecture

Inductive reasoning

Deductive reasoning

Counterexample

An unproven statement that is based on observations

When you find a pattern in a specific cases and then write a…

When you use facts and laws for a general case

Is a specific case for which the conjecture is false

Conjecture

An unproven statement that is based on observations

Inductive reasoning

When you find a pattern in a specific cases and then write a…