# 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

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

proof

two-column proof

congruent segments

congruent

a convincing argument that uses deductive reasoning.

lists each statement on the left and the justification for eac…

segments with equal lengths (or ≅)... congruent segments can be…

the same shape and size. ... two shapes are congruent when you ca…

proof

a convincing argument that uses deductive reasoning.

two-column proof

lists each statement on the left and the justification for eac…

Definition of Congruence

Segment Addition Postulate of Congruence

Reflexive Property of congruence

Addition Property

If PQ = PQ, then PQ ≅ PQ

If K is between J and L, then JK + KL = JL

EF ≅ EF

If RS = TU, then RS + XY = TU + XY

Definition of Congruence

If PQ = PQ, then PQ ≅ PQ

Segment Addition Postulate of Congruence

If K is between J and L, then JK + KL = JL

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

algebraic proof

addition property

subtraction property

multiplication property

a proof that is made up of algebraic statements.

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

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

If a = b, then a(c) = b(c)

algebraic proof

a proof that is made up of algebraic statements.

addition property

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

Congruent Segments

Congruent angles

Midpoint definition

Angle Bisector definition

Segments that have the same length- If the diagram says PQ = R…

Angles that have the same length- If the diagram says m∠ABC =…

If T is the midpoint of CE, then CT=TE ... (vice versa)

→... TP is the bisector of ∠RTE, then ∠RTP= ∠PTE ... (vice versa)

Congruent Segments

Segments that have the same length- If the diagram says PQ = R…

Congruent angles

Angles that have the same length- If the diagram says m∠ABC =…

Deductive Reasoning

Inductive Reasoning

Example Inductive Reasoning

Conjecture

Apply definitions, general statements, and already proven theo…

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

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

A conclusion developed by generalizing an idea using the induc…

Deductive Reasoning

Apply definitions, general statements, and already proven theo…

Inductive Reasoning

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

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

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

Division Property of Equality

Distributive Property of Equality

Midpoint theorem of Definition of Midpo…

Supplementary Angles

If a = b... Then a/3 = b/3

If a (b + c)... Then ab + ac

If M is the midpoint of AB, Then AM = MB ... CONVERSE OF THE THE…

Two angles that add up to be 180 degrees

Division Property of Equality

If a = b... Then a/3 = b/3

Distributive Property of Equality

If a (b + c)... Then ab + 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

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 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

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

reflective property of =

substitution property of =

symmetric property of =

transitive property of congruence/ =

any value is equal to itself

x=y x+5=7 then y+5=7

x=y then y=x

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

reflective property of =

any value is equal to itself

substitution property of =

x=y x+5=7 then y+5=7

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…

Addition property

Subtraction property

Multiplication property

Division property

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 ... then a/c=b/c ... (iif c does not equal 0)

Addition property

If a=b ... then a+c=b+c

Subtraction property

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

Conjecture

Counterexample

Inductive Reasoning

Deductive Reasoning

Unproven statement that is based on observations

Example that shows the conjecture is false

Process which includes looking for patterns... Example: All birds…

Process which includes facts, definition, accepted properties…

Conjecture

Unproven statement that is based on observations

Counterexample

Example that shows the conjecture is false

negation

converse

inverse

contrapositive

opposite of original statement; written as if not p, then q

switched order; if q, then p

opposite of p and q; if not p, then not q

converse then inverse; if not q, then not p

negation

opposite of original statement; written as if not p, then q

converse

switched order; if q, then p

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