Question | Answer |
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. |