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Proofs Study Quiz
Terms in this set (29)
Additive Identity Property
Multiplicative Identity Property
Commutative Property of Addition
Commutative Property of Multiplication
Distributive property of multiplication over addition
Addition Property of Equality
Subtraction Property of Equality
Multiplication property of equality
Division Property of Equality
A=B for any A or B
A part of a line with 2 endpoints and all points between them
Segments that have the same length
A point that divides a line segment into 2 congruent parts
A line/line segment/ray/plane that intersects a line segment at the midpoint
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
AB=CD, CD=EF, AB=EF
If C is between A and B then AC+CB=AB
Segment addition postulate
The length of a segment is equal to the absolute value of the difference of the endpoints
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A statement or sentence using a hypothesis (p) and conclusion (q). Some forms of this are 'if p, then q', 'p only if q', 'p implies q', and 'q if p'. A false ___ will have a true hypothesis but a false conclusion. Only one counterexample (an example that disproves a conjecture) is needed to prove this false.
A conditional statements which swaps the order of the hypothesis and conclusion. It changes the statements into 'if q, then p', 'q only if p', 'q implies p', and 'p if q'.
A conditional statement in which both the hypothesis and conclusion have been negated. It changes the statements into 'if not p, then not q', 'not p only if not q', 'not p implies not q', and 'not q if not p'.
when you take the converse of a conditional statement and negate the hypothesis and conclusion. It changes the statements into 'if not q, then not p', 'not q only if not p', 'not q implies not p', and 'not p if not q'.
a statement that can be written in the form "p if and only if (iff) q." you must base it on a true conditional statement and a true converse of the statement. For it to be false, either the conditional statement or converse of the statement must be false. All geometric definitions can be written as true ___statements.
The process of making observations of patterns to reason that a statement or conjecture (a statement that is unproven) is true.
The process of using logic to draw conclusions from given facts, definitions, and properties. It is used to prove a conditional statement or conjecture true, and to do so uses 2 laws.
If 'if p, then q' is a true statement, then for a specific p that is given is true, then q is true.
Law of Detachment
It draws conclusions from 2 conditional statements. To be applied, the conclusion of one statement must be the hypothesis of the other. The statements can be in any order. If 'if p, then q' and 'if q, then r' are both true conditional statements, then for a true p, 'if p, then r' is a true statement.
Law of Syllogism
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