How can we help?

You can also find more resources in our Help Center.

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

SSS

SAS

Angle addition postulate

Segment Addition Postulate

postulate stating that when two triangles have corresponding…

Triangles are congruent if any pair of corresponding sides an…

If point B lies in the interior of angle AOC, then. . The pos…

SAP, if B is between segment AC, then AB+BC=AC

SSS

postulate stating that when two triangles have corresponding…

SAS

Triangles are congruent if any pair of corresponding sides an…

Law of Detachment

Law of Syllogism

Two Point Postulate

Line-Point Postulate

If the hypothesis of a true conditional statement is true, th…

Take two conditional statements and form a conclusion by comb…

Through any two points, there exists exactly one line.

A line contains at least two points.

Law of Detachment

If the hypothesis of a true conditional statement is true, th…

Law of Syllogism

Take two conditional statements and form a conclusion by comb…

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

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 doesnt equal 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

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

inductive reasoning

conjecture

counterexample

statement

A type of logic in which generalizations are based on a large…

A guess based on incomplete evidence

an example that proves a statement false

A sentence that is either true or false.

inductive reasoning

A type of logic in which generalizations are based on a large…

conjecture

A guess based on incomplete evidence

Isosceles triangle

equilateral triangle

right triangle

rhombus

show that 2 sides are =. Use distance formula

show that 3 sides are =. Use distance formula

show that there is 1 right angle. Use slope formula

show that 4 sides are =. Use distance formula

Isosceles triangle

show that 2 sides are =. Use distance formula

equilateral triangle

show that 3 sides are =. Use distance formula

Right Angle Congruence Theorem(RACT)

Vertical Angle Congruence Theorem(VACT)

Linear Pair Postulate(LPP)

Congruent (Comp.,Supp.) theorem

right angles are congruent

vertical angles are congruent

if 2 angles are a linear pair then they are supplementary

If two angles are (Comp.,Supp.) of the same angle then they a…

Right Angle Congruence Theorem(RACT)

right angles are congruent

Vertical Angle Congruence Theorem(VACT)

vertical angles are congruent

A state meant that can be written in a…

Part "p" of the statement comes after If

Part "q" of the statement comes after…

Using pattern and observations to dete…

Conditional Statement

Hypothesis

Conclusion

Inductive Reasoning

A state meant that can be written in a…

Conditional Statement

Part "p" of the statement comes after If

Hypothesis

Congruent Segements

Congruent Angles

Adjacent angles

Linear Pair

2 segments with the exact same lengths

2 angles that have the exact same measurement

2 angles with a common vertex point and common side

Pair of adjacent angles whose no common sides are opposite rays

Congruent Segements

2 segments with the exact same lengths

Congruent Angles

2 angles that have the exact same measurement

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

Isosceles triangle

Equilateral triangle

Right triangle

What type of lines form a right angle?

SHOW: ... - 2 sides = ... FORMULA: ... - Distance

SHOW:... - 3 sides = ... FORMULA: ... - Distance

SHOW: ... - 1 right angle... FORMULA: ... - Slope

Perpendicular Lines

Isosceles triangle

SHOW: ... - 2 sides = ... FORMULA: ... - Distance

Equilateral triangle

SHOW:... - 3 sides = ... FORMULA: ... - Distance

definition of congruent segments

definition of congruent angles

definition of right angle

definition of midpoint

AB is congruent to CD... AB is equal to CD

m<ABC = m<DEF... <ABC is congruent to <DEF

<ABC is a right angle... m<ABC = 90 degrees

M is the midpoint of AB... AM is congruent to MB

definition of congruent segments

AB is congruent to CD... AB is equal to CD

definition of congruent angles

m<ABC = m<DEF... <ABC is congruent to <DEF

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

Isosceles Triangle

Equilateral Triangles

Right Triangle

Rhombus

2 sides are equal, Distance Formula

3 sides are equal, Distance Formula

1 right angle, slope

4 sides are equal, Distance Formula

Isosceles Triangle

2 sides are equal, Distance Formula

Equilateral Triangles

3 sides are equal, Distance Formula

reflexive property of equality

symmetric property of equality

transitive property of equality

substitution property of equality

AB=AB

If AB=CD, then CD=AB

If a=b and b=c, then a=c

If a=b, then a may be replaced by b in any equation or expres…

reflexive property of equality

AB=AB

symmetric property of equality

If AB=CD, then CD=AB

Complementary Angles

Supplementary Angles

Theorem

Vertical Angles

Two angles whose measures have a sum of 90 degrees

Two angles whose measures have a sum of 180 degrees

A statement that can be proven

Two angles formed by intercepting lines and facing in the opp…

Complementary Angles

Two angles whose measures have a sum of 90 degrees

Supplementary Angles

Two angles whose measures have a sum of 180 degrees

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"…

Linear Pair

Complementary

Supplementary

Right Angle

Two angles that are supplementary and adjacent

Two angles whose measure is equal to 90 degrees

Two angles whose measure is equal to 180 degrees

Angle whose measure is equal to 90 degrees

Linear Pair

Two angles that are supplementary and adjacent

Complementary

Two angles whose measure is equal to 90 degrees

Reflexive Property

Transitive Property

Symmetric Property

Addition Property of Equality

A quantity is equal to itself.

If two quantities are equal to the same quantity, then they a…

If a quantity is equal to a second quantity, then the second…

If equal quantities are added to equal quantities, then the s…

Reflexive Property

A quantity is equal to itself.

Transitive Property

If two quantities are equal to the same quantity, then they a…

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…

supplement therom

complemnt therom

congruent supplement therom

congruent complemnts therom

two angles form a linear pair

two adjecent angles form a right angle

if two angles are sup. to the same angle then the angles are…

if 2 angles are comp. to the same angle then the angles are c…

supplement therom

two angles form a linear pair

complemnt therom

two adjecent angles form a right angle

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

Definition of Congruence

Definition of Midpoint

Definition of Segment Bisector

Definition of Angle Bisector

A line segment or a line are congruent to another if and only…

If a line segment's midpoint is given, it is split into two e…

If a line, line segment, or plane bisects a segment, then it…

If a line, line segment, or plane bisects an angle, then it w…

Definition of Congruence

A line segment or a line are congruent to another if and only…

Definition of Midpoint

If a line segment's midpoint is given, it is split into two e…

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

Segment addition postulate

Definition of midpoint

Definition of segment bisector

Definition of congruent segments

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

P is the midpoint of segment AB and segment AP ≅ PB

A line, segment, ray, or plane that intersects the segment at…

DE ≅ FG... DE = FG

Segment addition postulate

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

Definition of midpoint

P is the midpoint of segment AB and segment AP ≅ PB

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, 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

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 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

counter examples

conditional statement

a type of reasoning that uses paterns to arrive at a conclusi…

the conclusion statement that was reached after incuctive rea…

an example that proves a statement to be false

a statement that can be written in if-then form. (P --> Q)

Inductive reasoning

a type of reasoning that uses paterns to arrive at a conclusi…

conjecture

the conclusion statement that was reached after incuctive rea…

conjecture

counterexample

deductive reasoning

inductive reasoning

a conclusion formed by reasoning

an observation that disrupts of challenges the observed

the process of using logic to arrive at a conclusion

using patterns to form a conclusion

conjecture

a conclusion formed by reasoning

counterexample

an observation that disrupts of challenges the observed

Supplementary angles

Linear pair

Complementary angles

Congruent angles

a pair of angles that sum to 180

a pair of adjacent angles that form a straight line, and thus…

a pair of angles that sum to 90

if a pair of angles have the same measure, then they are cong…

Supplementary angles

a pair of angles that sum to 180

Linear pair

a pair of adjacent angles that form a straight line, and thus…

angle

Adjacent Angles

Alternate Exterior Angles

Alternate Interior Angles

Angles are created by two distinct rays that share a common e…

Angles in the same plane that have a common vertex and a... comm…

Alternate exterior angles are pairs of angles formed... when a t…

Alternate interior angles are pairs of angles formed... when a t…

angle

Angles are created by two distinct rays that share a common e…

Adjacent Angles

Angles in the same plane that have a common vertex and a... comm…