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Conjecture
Unproven statement that is based on observations
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Inductive reasoning
use it when you find a patteren in specific cases and then write a conjucture for the general case
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counterexample
a specific case for which the conjecture is false
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conditional statement
LOGICAL STATEMENT THAT HAS TWO PARTS, A HYPOTHESIS AND A CONCLUSION
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if then form
The "if " part containts the hypothesis and the then part contains the conclusion
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Converse
- If < A is obtuse then M< A =99
- where you switch the two
- exchange the hypothesis and conclusion
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Inverse
- Nagate both the Hypothesis and the conclusion
- if m not equal to 99 theh <a is not obtuse
- make both negitive in the same order
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contrapositive
- You first write the converse and then negate bothe the hypothesis and the conclusion
- if <a ia not obtuse then M< A is not 99
- you switch them and make both negitive.
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Perpendicular lines
Two lines that intersect to from a right angle
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equivalent statements
When two statements are both true or both false.
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Biconditional statement
A statement that contains the phrase "if and only if"
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definition: If two lines intersect to form a right angle, then they are perpendicular lines
converse:
Biconditional:
- converse: if two lines are perpendicular, then they intersct to form a right angle
- Biconditional: Two lines are perpendicular if and only if they intersect to from a right angle
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Deductive reasoning
uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.
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Law of detachment
If the hypothesis of a true conditional statement is true, then the conclusion is also true.
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Law of syllogism
- If Hypothesis p, then conclusion q
- If Hypothesis q, then conclusion r.
- If hypotesis q then conclusion r.
if the top two are true then the bottom is also true
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Postulates or axioms
rules that are accepted without proofs.
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Theorems
rules that are proved
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A Line perpendicular to a plane
If and only if the line intercects the plane in a point and is perpendicular to every line in the plane that interscts it at theat point.
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Addition property
if a=b then a+c=b+c
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subtraction propertey
if a=b then a-c= b-c
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multiplication property
if a=b then ac=bc
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division propertey
if a=b and c is not equal to 0 the a/c=b/c
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subsitution property
if a=b then a can be subsituted for b in any equation or expression
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proof
logical argument that shows a statement is true
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two column proof
has numbered statment and corresponding reason that show an argument in a logical orger
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theorem
statement that can be proven
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congreence of segments
reflexive:
Symmetric:
Transitive:
- reflexive: for an seg. ab, ab is congrent to Ab
- Symmetric: If seg AB is cong to CD then CD is cong to AB
- Transitive: If seg AB is cong to CD and CD is cong to EF then seg AB is con to EF
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Right angle congruence theorem
all right angels are congrent
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Congruent supplement theorem
- if two angle are supplementary to the same angle then they are congrent
- If <4 and <5 are complemtrarty and <6 and <5 are complemtry then <4 is congrent to <6`
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Linear pair Postulate
- If two angles for a liner pair, then they are supplementery
- <1 and <2 form a linear pair, so <1 and <2 are supplementary and M<1 + M<2 = 180
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Vertical angles congruence theorem
vertical angles are congruent
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