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Perpendicularity

Complimentary Angles

Supplementary Angles

Adjacent Angles

Lines, rays and segments that intersect at right angles

Angles whos sum is 90 degrees

Angles who's sum is 180 degrees

Share a common side or ray

Perpendicularity

Lines, rays and segments that intersect at right angles

Complimentary Angles

Angles whos sum is 90 degrees

inductive reasoning

conjecture

conditional

counterexample

reasoning based on patterns you observe

a conclusion you reach using inductive reasoning

if p then q

example that proves that a conclusion is not true

inductive reasoning

reasoning based on patterns you observe

conjecture

a conclusion you reach using inductive reasoning

conditional statement

hypothesis

conclusion

converse

This has 2 parts, a hypothesis and a conclusion.

The "if" part of a conditional statement

The "then" part of a conditional statement.

This is formed when you switch the hypothesis and conclusion…

conditional statement

This has 2 parts, a hypothesis and a conclusion.

hypothesis

The "if" part of a conditional statement

Linear Pair

Perpendicular

Complementary Angles

Supplementary Angles

If ray AB and ray AC are opposite rays and D is a point not o…

Lines, rays, or segments that intersect to form right angles.

Two angles whose sum is 90.... m angle 1 + m angle 2 = 90

Two angles whose sum is 180.... m angle 1 + m angle 2 = 180

Linear Pair

If ray AB and ray AC are opposite rays and D is a point not o…

Perpendicular

Lines, rays, or segments that intersect to form right angles.

2.1 Through any two points, there is e…

2.2 Through any three noncollinear poi…

2.3 A line contains at least two points

2.4 A plane contains at least three no…

Line N is the only line through points P and R

Plane K is the only plane through noncollinear points A, B an…

Line N contains points P, Q and R

Plane K contains noncollinear points L, B, C and E

2.1 Through any two points, there is e…

Line N is the only line through points P and R

2.2 Through any three noncollinear poi…

Plane K is the only plane through noncollinear points A, B an…

perpendicular

complementary angles

supplementary angles

if two angles are supplementary to the…

lines, rays, or segments that intersect at a right angle

if two angles sum is 90 degrees then each of the two angles a…

if two angles sum is 180 degrees then each of the two angles…

perpendicular

lines, rays, or segments that intersect at a right angle

complementary angles

if two angles sum is 90 degrees then each of the two angles a…

conjecture

inductive reasoning

counterexample

conditional statement

unproven statement that is based on an observation

A type of reasoning that reaches conclusions based on a patte…

specific case for which the conjecture is false

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

conjecture

unproven statement that is based on an observation

inductive reasoning

A type of reasoning that reaches conclusions based on a patte…

inductive reasoning

conjecture

conditional

truth value

reasoning based on patterns you observe

a conclusion you reach using inductive reasoning

if p then q

true or false

inductive reasoning

reasoning based on patterns you observe

conjecture

a conclusion you reach using inductive reasoning

Inductive Reasoning

Conjecture

Counterexample

Statement

Making a conclusion based on observations and patterns.

A concluding statement reached using inductive reasoning.

An example that shows a conjecture is false.

A sentence that is either true or false.

Inductive Reasoning

Making a conclusion based on observations and patterns.

Conjecture

A concluding statement reached using inductive reasoning.

conjecture

inductive reasoning

counterexample

conditional statement

an unproven statement that is based on observations

when you find a pattern in specific cases and then write a co…

a specific case for which the conjecture is false

a logical statement that has a hypothesis and a conclusion

conjecture

an unproven statement that is based on observations

inductive reasoning

when you find a pattern in specific cases and then write a co…

if then statement (conditional stateme…

hypothesis

conclusion

converse

-has a condition containing a hypothesis and a conclusion

-the part following the "if"... -describes the condition necessa…

-the outcome when the hypothesis is present... -the part followi…

-the converse of a conditional is found by switching the hypo…

if then statement (conditional stateme…

-has a condition containing a hypothesis and a conclusion

hypothesis

-the part following the "if"... -describes the condition necessa…

Conditional Statement

If-then form

Negation

Equivalent Statements

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

The "if" part contains the hypothesis and the "then" part con…

A statement that is the opposite of the original statement.…

When two statements are both true or both false.

Conditional Statement

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

If-then form

The "if" part contains the hypothesis and the "then" part con…

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair

2 angles where the sum of their measures is 90

2 angles where the sum of their measures is 180

2 angles with a common side

A pair of adjacent angles where the non-common sides form a l…

Complementary Angles

2 angles where the sum of their measures is 90

Supplementary Angles

2 angles where the sum of their measures is 180

conditional statements

converse of a conditional statement

hypothesis

conclusion

a statement whose basic form is if p then q. ... made up of hyp…

changing of the hypothesis and conclusion from the original s…

part of a conditional statement ... (after if)

part of a conditional statement... (after then)

conditional statements

a statement whose basic form is if p then q. ... made up of hyp…

converse of a conditional statement

changing of the hypothesis and conclusion from the original s…

Inductive Reasoning

Conjecture

Counterexample

Statement

Forming conjectures on the basis of observation.

A statement believed to be true.

An example that proves a statement is false.

A sentence that is either true or false.

Inductive Reasoning

Forming conjectures on the basis of observation.

Conjecture

A statement believed to be true.

Conditional Statements

Hypothesis

Conclusion

Shorthand for conditional statements

An "If...then" statement.

The "If" part of a conditional statement.... (Does not include t…

The "Then" part of a conditional statement... (Does not include…

"p-->q" ... Read as: "If P then Q" or... "P implies Q"

Conditional Statements

An "If...then" statement.

Hypothesis

The "If" part of a conditional statement.... (Does not include t…

Conjecture

Indeductive Reasoning

Counterexample

Conditional statement... a. converse... b.…

A statement that is believed to be true but not yet proved.

A form of reasoning in which a conclusion is reached based on…

Counterexample is an example that is used to disprove a state…

symbolized by p q, is an if-then statement in which p is a hy…

Conjecture

A statement that is believed to be true but not yet proved.

Indeductive Reasoning

A form of reasoning in which a conclusion is reached based on…

perpendicular

complementary angles

supplementary angles

if two angles are supplementary to the…

lines, rays, or segments that intersect at a right angle

if two angles sum is 90 degrees then each of the two angles a…

if two angles sum is 180 degrees then each of the two angles…

perpendicular

lines, rays, or segments that intersect at a right angle

complementary angles

if two angles sum is 90 degrees then each of the two angles a…

five things that can be used as reason…

reflexive property

symmetric property

transitive property

given, properties, definitions, postulates, theorem

ab=ab

if a=b, then b=a

if a=b and b=c then a=c

five things that can be used as reason…

given, properties, definitions, postulates, theorem

reflexive property

ab=ab

Congruency of supplementary angles (Th…

Supplementary congruent angles... (Theore…

Congruent complementary angles (Theore…

Congruency of complementary angles (Th…

If angles that are supp. To the same angle then they are cong…

If angles are supp. to congruent angles then, they are congru…

If angles complementary to the same angle, then they are cong…

If angles are complementary to congruent angles then they are…

Congruency of supplementary angles (Th…

If angles that are supp. To the same angle then they are cong…

Supplementary congruent angles... (Theore…

If angles are supp. to congruent angles then, they are congru…

Conjecture

Inductive Reasoning

Counterexample

Conditional Statement... a. Converse... b.…

A statement that is believed to be true but not yet proved

A statement about geometry that is accepted as true without p…

an example that is used to disprove a statement.

symbolized by p q, is an if-then statement in which p is a hy…

Conjecture

A statement that is believed to be true but not yet proved

Inductive Reasoning

A statement about geometry that is accepted as true without p…

Theorem (Number Unknown, Coplanar perp…

All rt ∠'s are ≅

Midpoint Theorem

Angle Bisector Theorem

If P is an element of line l, then there exists only one uniq…

If ∠1 and ∠2 are right angles, then ∠1≅∠2

If M is the midpoint of segment AB, then AM=1/2(AB) and 2AM=AB

If ray BP bisects ∠ABC, then m∠ABP=1/2(m∠ABC) and 2m∠ABP=m∠ABC

Theorem (Number Unknown, Coplanar perp…

If P is an element of line l, then there exists only one uniq…

All rt ∠'s are ≅

If ∠1 and ∠2 are right angles, then ∠1≅∠2

Inductive Reasoning

Deductive Reasoning

Conjecture

Counterexample

Reach a conclusion based on analysis of a pattern; doesn't us…

Involves the usage of rules and formulas; uses the "n" in pat…

Unproven statement based on examples in a pattern ... Example:…

Example that disproves the conjecture (makes it not true) ... E…

Inductive Reasoning

Reach a conclusion based on analysis of a pattern; doesn't us…

Deductive Reasoning

Involves the usage of rules and formulas; uses the "n" in pat…

inductive reasoning

deductive reasoning

conjecture

conditional statement

the process of observing data, recognizing patterns, and maki…

the process of showing that certain statements follow logical…

a generalization based on inductive reasoning

if/then statement

inductive reasoning

the process of observing data, recognizing patterns, and maki…

deductive reasoning

the process of showing that certain statements follow logical…

Perpendicular

Oblique lines

Coordinate axes

Orthogonal

Lines, rays, segments that intersect at right angles

Lines, Rays, segments, that intersect but not at right angles

Perpendicular examples?

Perpendicular...AKA:

Perpendicular

Lines, rays, segments that intersect at right angles

Oblique lines

Lines, Rays, segments, that intersect but not at right angles

inductive reasoning

conjecture

counterexample

statement

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

concluding statement reached using inductive reasoning

false example that can be a drawing, number, or statement

sentence that is either true or false

inductive reasoning

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

conjecture

concluding statement reached using inductive reasoning

conditional statement

hypothesis

conclusion

converse

statement that can be written in the form "if p, then q."... p o…

part p of a conditional statement following the word if

part q of a conditional statement following the word then

statement found formed by exchanging he hypothesis and conclu…

conditional statement

statement that can be written in the form "if p, then q."... p o…

hypothesis

part p of a conditional statement following the word if

Conjecture

Inductive reasoning

Counter-example

Statement

An educated guess based on known information

Using several specific situations to arrive at a conjecture

An example that shows that the conjecture is false

Any sentence that is either true or false

Conjecture

An educated guess based on known information

Inductive reasoning

Using several specific situations to arrive at a conjecture

Conditional Statements

Converse

Biconditional

Reflexive Property

Hypothesis & Conclusion

conditional formed by switching the order (aren't always true)

REVERSIBLE: postulates, theorems and definitions are bicondit…

a=a or a is congruent to a

Conditional Statements

Hypothesis & Conclusion

Converse

conditional formed by switching the order (aren't always true)

conditional statement

if-then statement

hypothesis

conclusion

statement that can be written in if-then form

written in the form if p, then q

the phrase immediately following the word if

the phrase immediately following the word then

conditional statement

statement that can be written in if-then form

if-then statement

written in the form if p, then q

conjecture

inductive reasoning

counterexample

conditional statement

an unproven statement that is based on observations

when you find a pattern in specific cases and then write a co…

a specific case for which the conjecture is false

a logical statement that has a hypothesis and a conclusion

conjecture

an unproven statement that is based on observations

inductive reasoning

when you find a pattern in specific cases and then write a co…

Complement

Complementary angle

Coordinates

Oblique lines

the two angles whose sums are 90° are complements of each oth…

either of two angles whose sum is 90°.

a group of numbers used to indicate the position of a point,…

When two lines intersect but are not perpendicular.

Complement

the two angles whose sums are 90° are complements of each oth…

Complementary angle

either of two angles whose sum is 90°.

Conjecture

Inductive Reasoning

Counterexample

Conditional Statement

An unproven statement based on observations

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

A specific case where a conjecture is false

A logical statement that has a Hypothesis and a Conclusion

Conjecture

An unproven statement based on observations

Inductive Reasoning

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

inductive reasoning

conjecture

counterexample

conjunction

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

conclusion based upon inductive reasoning

one example that shows the conjecture is false

when both the hypothesis and the conclusion must be true for…

inductive reasoning

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

conjecture

conclusion based upon inductive reasoning

inductive reasoning

conjecture

counterexample

conditional statement

the process of reasoning that a rule or statement is true bec…

a statement you believe to be true based on inductive reasoning

the one example that proves the conjecture false

a statement that can be written in the form "if p, then q"

inductive reasoning

the process of reasoning that a rule or statement is true bec…

conjecture

a statement you believe to be true based on inductive reasoning

Consecutive Interior Angles

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Interior angles that lie on the same side of transveral

nonadjacent interior angles that lie on opposite sides of tra…

nonadjacent exterior angles that lie on opposite sides of tra…

lie on the same side of traversal and on the same lines

Consecutive Interior Angles

Interior angles that lie on the same side of transveral

Alternate Interior Angles

nonadjacent interior angles that lie on opposite sides of tra…

Reflexive Property of Congruence (Theo…

Symmetric Property of Congruence (Theo…

Transitive Property of Congruence (The…

Congruent Supplements (Theorem)

Angle 1 = Angle 1

If Angle 1 = Angle 2, then Angle 2 = Angle 1

If Angle 1 = Angle 2 and Angle 2= Angle 3, then Angle 1 = Ang…

Angles supplementary to the same angle or to congruent angles…

Reflexive Property of Congruence (Theo…

Angle 1 = Angle 1

Symmetric Property of Congruence (Theo…

If Angle 1 = Angle 2, then Angle 2 = Angle 1

Inductive reasoning

Conjecture

Counterexample

conditional

reasoning baed on patterns you observe

a conclusion you reach using inductive reasoning

an example that shows a conjecture is correct

an if-then statement (p implies q)

Inductive reasoning

reasoning baed on patterns you observe

Conjecture

a conclusion you reach using inductive reasoning

Compound statement

Conjecture

Disjunction

Inverse

A statement formed by joining two or more statements

An educated guess based on known information

A compound statement formed by joining two or more statements…

The statement formed by negating both the hypothesis and conc…

Compound statement

A statement formed by joining two or more statements

Conjecture

An educated guess based on known information

inductive reasoning

conjecture

counter example

conditional

reasoning based on patterns you observe

a conclusion you reach using inductive reasoning

an example that shows a conjecture is incorrect

an if-then statement using the symbol p-->q

inductive reasoning

reasoning based on patterns you observe

conjecture

a conclusion you reach using inductive reasoning

Inductive Reasoning

Conjecture

Statement

Truth value

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

A concluding statement reached using inductive reasoning

A sentence that is either true or false

Whether the statement is true or false

Inductive Reasoning

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

Conjecture

A concluding statement reached using inductive reasoning

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…