22pintri

How To Use Basic Logic in Geometry

A very helpful link to every postulate and theorem which will cover this [|lesson]head to toe!

__Introducing Proofs__
 * Section #1**

Key Concept: Proving Your Point – Ex. Proving that a chessboard with 64 squares can hold 32 regular sized dominoes is a problem that are famous mathematical questions.



Figure that two squares are cut from opposite corners of a chessboard. Can the remaining squares be completely covered by 31 dominoes? If you answer yes, you must provide a method for showing your it’s possible. If your answer is no, you must explain why it cannot be done. Either of the two choices would be proved by setting up a proof.

__Key Wording:__ Proof – Is a convincing argument that something is true.

__Introducing Logic__
 * Section #2**



__Key Wording:__ Conditionals – A statement using “if-then” in it (If I hit home runs, then I play baseball)

Hypothesis – In a conditional, the part following the word “if” is the hypothesis. (I hit homeruns)

Conclusion – In a conditional, the part following the word “then” is the conclusion. (I play baseball)

Deductive Reasoning/Deduction – The process of drawing logically certain conclusions by using an argument.

Euler Diagram – Euler Diagram, also called Venn Diagram, is a picture way to show that a statement is true.

Converse – When you interchange the hypothesis and the conclusion of a conditional, it turns into the converse.

Counterexample – An example that proves that a statement is false is the counterexample.

Logical Chain – When conditionals are linked together, they form a logical chain.

__If-Then Transitive Property:__ Given: If A, then B, and If B, then C You can conclude: If A, then C

__Introduction to Definitions
 * Section #3**



Key Wording:__ Biconditional - The statement of "If and only If" resulting from a true conditional. Ex. If someone was to tell another person to group items in a certain way, they may say something like, "Put all the items in the blue box __if and only if__ they are yellow colored"

__The System of Geometry__
 * Section #4**

__Algebraic Properties of Equality:__ Addition Property - If a=b, then a+c = b+c Subtraction Property - If a=b, then a-c = b-c Multiplication Property - If a=b, then ac = bc Division Property - If a=b, and c does not = 0, then a/c = bc Substitution Property - If a = b, you may replace a with b in any true equation with a involved, and the new equation will still be true.

__Overlapping Segments Theorem:__ The following statments corresponding to the picture will always be true.

A--B--C--D If AB = CD, then AC = BD If AC = BD, then AB = CD



__Equivalence Properties of Equality:__ Reflexive Property - For any real number (a), a = a Symmetric Property - For all real numbers (a) and (b), if a = b, then b = a Transitive Property - For all real numbers (a),(b),(c), if a = b and b = c, then a = c

All of the above statements are used to tell which property relates 2 or possibly more object together.

Section #5 __Introducing Conjectures and Theorems__

__Key Wording:__ Vertical Angles - Vertical angles are 2 opposite angles from by 2 intersecting lines. Vertical angles are always congruent.



__Congruent Supplements Theorem:__ If 2 angles are supplementary of congruent angles, then the 2 angles are congruent.

The use of all theorems etc. is to have a true reason and explanation for being able to arrive at a specific outcome or answer.