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51 Cards in this Set
- Front
- Back
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A statement |
If A, then B. |
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Converse of the statement |
If B, then A. |
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Inverse of a statement |
If not A, then not B. |
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Contrapositive of a statement |
If not B, then not A. |
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Conjecture |
An unproven statement based on observations |
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Inductive Reasoning |
When you find a pattern in specific cases and then write a conjecture for the general case |
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Counterexample |
A specific case for when the conjecture is false |
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How to find the conjecture |
By making the hypothesis right, but the conclusion false. A= hypothesis B= conclusion. |
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Conditional statement |
A logical statement that has two parts, a hypothesis and a conclusion. When it is written in the IF-THEN form, the hypothesis is the IF and the conclusion is the THEN. |
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Negation statement |
The opposite of the original statement. Ex) the ball is red Negation: the ball is not red |
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Converse and inverse are generally ____. |
Both true or both false |
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The conditional statement and the contrapositive statement are usually _____. |
Both true or both false. |
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In general, when two statements are both false or both true, they are called |
Equivalent statements |
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Biconditional statement |
WHEN A CONDITIONAL STATEMENT AND ITS CONVERSE IS BOTH TRUE, YOU CAN WRITE THEM AS A BICONDITIONAL STATEMENT. A BICONDITIONAL STATEMENT CONTAINS THE PHRASE IF AND ONLY IF. ex) definition: if two lines intersect to form a right angle, then they are perpendicular. converse: if two lines are perpendicular, then they intersect to form a right angle. Biconditional: Two lines are perpendicular IF and only IF they intersect to form a right angle. |
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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 p then r if r then q if p then q |
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Inductive reasoning |
when you find a pattern in specific cases and then write a conjecture on it (experiment) |
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Definition of perpendicular lines |
If two lines intersect to form a right angle, then they are perpendicular lines |
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Deductive reasoning |
uses facts, definitions, accepted properties, and the laws of logic to form a logical argument (using facts) |
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Addition Property |
if a=b then a+c=a+b |
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Subtraction Property |
if a=b then a-c=a-b |
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Multiplication property |
If ab then ac=bc |
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Division property |
if a/b then a/c=a/b |
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substitution property |
if a=b then a can be substituted into any equation for b or any expression |
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Distributive property |
a(b+c) can be simplified as ab+ac |
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Theorem 2.1: Congruence of Segments |
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Reflexive Property of Equality |
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Symmetric property of equality |
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Transitive property of equality |
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Theorem 2.2: Congruence of angles |
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Theorem 2.3: Right Angles Congruence theorem |
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Theorem 2.4: Congruent supplements theorem |
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Theorem 2.5: Congruent complements theorem |
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Theorem 2.6: Vertical angles congruence theorem |
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Postulate 1: Ruler postulate |
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Postulate 2: Segment addition postulate |
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Postulate 3: Protractor Postulate |
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Postulate 4: Angle addition postulate |
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Postulate 12: Linear Pair postulate |
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Postulate 5 |
Through two points there exists one line |
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Postulate 6 |
A line contains at least 2 points |
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Postulate 7 |
If two lines intersect, then their intersection is exactly one point |
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Postulate 8 |
Through any 3 noncollinear points, there exists one plane |
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Postulate 9 |
A plane contains at least 3 noncollinear points |
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Postulate 10 |
If two points lie on a plane, then the line containing them lies on the plane |
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Postulate 11 |
If two planes intersect, their intersection is a line |
