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# Geometry Ch 2

### Stepp's Prentice Hall Geometry Chapter 2 Reasoning And Proof

conditional another name for if, then statements
hypothesis the part following "if" also represented by "p"
Conclusion the part following "then" represented by "q"
truth value true or false
converse statement obtained by switching p and q so that q implies p
biconditional when a statement and its converse are both true they can be combined into one statement with "if and only if"
Good Definitions are reversable
The arrow on a biconditional points both ways
If the converse is false you can not write a biconditional
the term conversely means the same as vica versa
deductive reasoning logically connecting given statements to the appropriate conclusions
Law of Detachment if a conditional is true, then the conclusion is true any time you find the hypothesis
Law of Syllogism if the conclusion of one statement is also the hypothesis of another statement then you can form a third conditional statement connecting the original hypothesis with the final conclusion
If p implies q and q implies r then p implies r
If p imples q is a true statement and you found p to be true then q must be true
If p implies q and you found q then you know nothing you can only make a conclusion when you are given p ( unless it was an "if and only if" statement)
iff means if and only iff, you have a biconditional (both the statemtent AND its converse are true
Addition Property of EQUALITY you can add the same quanity to both sides of an equation and the result is also true
Subtraction Property of EQUALITY you can subtract the same quanity from both sides of an equation and the result is also true
Multiplication Property of EQUALITY you can multiply both sides of an equation by the same quanity and the result is also true
Division Property of EQUALITY you can divide both sides of an equation by the same quanity and the result is also true
Reflexive Property of EQUALITY everything is equal to itself (you see your reflection in a mirror)
Symmetric Property of EQUALITY if a = b then b=a
Transitive Property of EQUALITY if two things are both equal to a third thing then they are also equal to each other
Substitution Property of EQUALITY if a=b then you can replace a with b anywhere
The Distributive Property a(b + c) = ab + ac
Properties of Congruence Reflexive, Symmetric, and Transitive properties are not only good for equality (with numbers) they also work with congruence (figures)
THEOREM A statement that you can prove to be true with deductive reasoning
Proof the set of steps you take to show a conjecture is true
Paragraph Proof written statements that are backed up by proper reasons to show a stateement is true
Two column proof form with numberd statements and corresponding reasons for making those statements
Given material or information that has been supplied to you. You assume it to be true because it was "GIVEN."
First reason in a two column proof given
Angle Addition Postulate part + part = whole angle
Last statement in a proof the prove statement
You have to have 2 conditionals to use the Law of Syllogism
Most common mistake using the Law of Detachment assuming the converse is true
A statemen you can prove true is a theorem
Vertical Angles are opposite angles formed by two intersecting lines and they are CONGRUENT
How do you write the two conditionals that form a biconditional first write the if, then statement, then write it's converse
checklist for angles vertical, supplementary, complementary, angle addition postulate.
Created by: criswell216