#### Study sets matching "chapter 2 geometry proofs"

#### Study sets matching "chapter 2 geometry proofs"

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"…

Theorem 2.1: Vertical Angles

Theorem 2.2: Congruent Supplements The…

Theorem 2.3: Congruent Complements The…

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 The…

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

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

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

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

Deductive Reasoning

Inductive Reasoning

Example Inductive Reasoning

Conjecture

Apply definitions, general statements, and already proven the…

A way of drawing a general conclusion from special cases by e…

All numbers in the set are multiplied by 3... The sum of the dig…

A conclusion developed by generalizing an idea using the indu…

Deductive Reasoning

Apply definitions, general statements, and already proven the…

Inductive Reasoning

A way of drawing a general conclusion from special cases by e…

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".

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

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…

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

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"…

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**Cproof

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

addition property of equality

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

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

theorem

two-column proof

Linear Pair Theorem

Congruent Supplements Theorem

any statement that you can prove

list the steps of the proof in the left column, and the match…

if two angles form a linear pair, then they are supplementary

If two angles are supplementary to the same angle (or to two…

theorem

any statement that you can prove

two-column proof

list the steps of the proof in the left column, and the match…

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…

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"…

Conditional statment

Form of a conditional statement

Form of a converse

Form of a negation

a statement that says one thing will result from another

if P, then Q.

if Q, then P.

not P

Conditional statment

a statement that says one thing will result from another

Form of a conditional statement

if P, then 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)

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…

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…

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 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.

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

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…

Reflexive property

Transitive property

Substitution property

Symmetric property

When everything equals itself (ex. <ab = <cd)

If a = B and B = c, then a = c

If a = b, then B can be substituted for A (or the other way a…

If a = b, then b = a

Reflexive property

When everything equals itself (ex. <ab = <cd)

Transitive property

If a = B and B = c, then a = c

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