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 =…
conjecture
inductive reasoning
deductive process
counterexample
an unproven statement that is based on observations
when you find a pattern in specific cases and then write a con…
logical process in which a conclusion is based off of
specific case for which the conjuncture is false
conjecture
an unproven statement that is based on observations
inductive reasoning
when you find a pattern in specific cases and then write a con…
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
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…
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
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
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
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
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
conditional statement
if-then form
hypothesis
conclusion
A logical statement that has a hypothesis and a conclusion.
A conditional statment in the form "if p, then q".
The "if" part of a conditional statement written in if-then fo…
The "then" part of a conditional statement in if-then form.
conditional statement
A logical statement that has a hypothesis and a conclusion.
if-then form
A conditional statment in the form "if p, then q".
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