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__//**Introduction to Proofs**//__



- investigate proofs of mathematical claims. -learn the meaning of the term proof.
 * Objectives**

__proof__- an argument that something is true.
 * Vocabulary:**

5×+4=24 Given 5×=20 Subtraction property of equality ×=4 Division property of equality
 * Examples**

http://www.download-free-games.com/board_game_download/clue.htm
 * Some fun math games:**

__//**Introduction to logic**//__

-If a fat bird sits - A tree breaks. - Then the horses spook.

-Learn the meaning of Conditionals and show them with Euler diagrams. -In logical arguments use conditionals. -Make the converse of conditionals. -Form logic chains using conditionals.
 * Objectives**

__Conditionals__- "If-then" statements are conditionals. __Hypothesis__- The word "if" is used. __Conclusion__- The word "then" is used. __Deductive reasoning__- logically certain conclusions using arguments also described as deduction. __Converse__-if you interchange the hypothesis adn the conclusion of a conditional then it is called the converse.
 * Vocabulary:**

Given: You can conclude if A then B, and if A then C. if B then C.
 * If- Then Transitive Property**

http://www.logicgamesonline.com/
 * Here is fun logic games:**

Their are many diffrent species of otters in the world.
 * //__Definitions__//**

-using euler diagrams study definitions of objects. -using principles of logic to cerate definitions of objects.
 * objectives**

__Converse-__by interchanging the hypothesis and conclusion you can write the converse of the conditional. __biconditional-__statements that are "if-and -only-if" __Adjacent Angles__- are angles htat have a comm ray that comes out of the vertex that goes between two other rays. http://www.mathleague.com/help/geometry/angles.htm#alternateexteriorangles
 * Vocabulary:**


 * //__System of geometry__//

objectives** -learn the algebraic properties of equality. - learn and use the equivalence properties of equality of congruence. -while using properties and postulates link the steps of a proof. __Algebraic Properties of Equality__ addition property- B = A, then B+C = A+C subtraction property- B =A, then B-C = A-C multiplication property- B =A, then BC =AC Division property- B = A and C =/ 0, thention B/C = A/C Substitution property- B = A, you may replace B with A in any correct equation contaning B and the resulting equation will still be true. __Overlaping Segments theorem__ You have a segment with points A, B,C, and D in htat order then the folling statements will be true. AB=CD, then AC=BD AC=BD, then AB=CD __Equivalence Properties of Equality__ reflexive property- for any real numbers a = a. symmetric property- all real numbers c and d, if c = d, then d = c. Trensitive propertyall real numbers q,w, and, e q = w and w = q, then q = e. __Equivalence properties of congruence__ Refleive property Figure D = figure D symmetric property Figure D = figure E then figure E = figure D Transitive property figure D = figure A and figure A = figure C then figure D = figure C __Overlaping angles theorem__ -if m<COD = m<AOB -if m<BOD = m<AOC
 * vocabulary:**

congruence links: http://regentsprep.org/Regents/math/congruen/Lcongruent.htm


 * //__Conjectures that go to Theorems__//

Objestives** - Theorems to conjectures. - Two-column and paragraph proofs.

__vertical angles__-the opposite angles that are made by two intersecting lines. for example: scissors __inductive reasoning__- making conjectures that are based on observation. __vertical angles__- they are congruent if two angles form a pair of virtical angles. __Reflection across tow parallel lines-__ tow parlaael lines is equal to a side of a double the distance between the lines and direction perpendicular to the lines. __congruent supplements__- the tow andgles are congruent if the two angles are supplements of congruent angles. http://en.wikipedia.org/wiki/Theorem
 * Vocabulary:**