By: Mateo Safie

A “IF THEN” statement that gives a hypothesis and a conclusion (The statement is not necessarily true) The hypothesis is represented by a “P” and is the first part of the sentence, or the “IF” part of the sentence. The conclusion is represented by a “Q” and is the second part of the sentence, or the “THEN”

If You jump off a roof, Then you will get hurt. If you have no money, Then you won’t buy. If you fail in your final, Then you don’t pass the year.

A counter example is a Example that shows that the statement is not true most of the time it disapproves the Hypothesis'’

All odd numbers are prime C-E: 21, 27, 33, etc. Every one lives on a house C-E: there is people who lives in apartment buildings or college dorms. Every criminal has bad intensions C-E: Robin Hood wanted to help the poor.

All definitions are bi-conditional (they are true from any perspective). They are used to make people understand what is “something”.

Def of a TV: a communication devise that uses a images and audio to transmit a message to anyone who is watching it. Def of school: a complex of buildings with teachers, were people assist to learn what the school teaches. Def of Examples: a example is a proof to a statement. Example for an example: pink like a pig (the pig skin is the example or the color pink)

A Bi-Conditional statement is a true conditional statement that Its converse is also true. Instead of Then we use: IF and only IF (IFF). It is used to show that the conclusion can be stated as hypothesis and vise versa. They are important because they are used by our logic, sometimes subconsciously and they are the bases of our “thinking”.

A shape is a square iff all 4 sides are equal. Mr. Turner is a teacher iff he gives class. I am human iff I communicate with other humans.

It is a human way of thinking were you look at facts to make a conclusion. Collect data or facts Look at them Make YOUR conclusion Symbolic notation is a simpler way to write down things, like: + plus - minus x times / divisions

They tell you that if your passport expires in 6 months or less you cant travel to other countries. Your passport expires and today ( ) you are traveling to the US. You know they will let you travel. You know you need money to live (nowadays). The only way to get money legally is working, then you know that live you need to find a job. They tell you that is you don’t pay to get in the park there will be consequences. You don’t want anything bad happening to you, therefore you pay to get in.

Law of detachment. Law of Syllogism.

If your statement is true, then you know that is your hypothesis is true your conclusion HAS to be true. If you commit a crime, Then you go to jail. Jack crashes a car and he was drunk.Q=Jack has to go to jail. If are short heighted then you can’t get on the roller coaster. Jimmy is only 3,9ft tall.Q=Jimmy can’t get in the coaster. If you are 16 or younger, then you cant play rated “m” games. John is 26. Q=John can play rated “m” games.

If your “hypothesis” then “conclusion”, and “hypothesis” then “conclusion” are both true statements, the if “hypothesis” is true then “other conclusion” is true. If you buy a gift, then you are nice. If you are nice then you might have good friends.Jerry buys a gift then he might have good friends. If it is your birthday, then you do a party. If you do a party, then you will have fun. Today it’s Mary's birthday, then she will have fun. If you have class with Mr. Turner, then you make journals. If you make journals, then you have to work hardMateo is in Mr. Turner class, then he has to work hard.

It is a logical argument that validates your statement or press of solving an equation. To do it: 1.They give you a given. 2.Then solve justifying every step until you get to what they want you to prove. properties of equality: Addition-add same num on both sides Subtraction-rest the same num on both sides Multiplication-times same num on both sides Division-divide the same num on both sides Reflexive- A=A symmetric A=B, B=A Transitive-A=B, B=C, A=C Substitution- if A=B we can replace one with the other.

statement 9x+2= x= x=2 reason Given -prop. Simplify /prop. simplify statement 19x-49= x= x=3 statement 9x= x=9 reason Given +prop. Simplify /prop. simplify reason Given /prop. simplify 2 column proofs

Transitive: If AB equal CD, and CD equal EF, then AB equal EF If AB congruent to CD and CD congruent to EF then AB congruent to EF. Symmetric: If TS equal PQ, then PQ equal TS. If TS congruent PQ, then PQ congruent TS Reflexive: MN = MN, MN congruent to MN

If M is the midpoint of ZA and A is the midpoint of MP then MZ is equal to AP. IF AC is equal to BT then BT is equal to AC. FR is always equal to FR. Z M A P A CB T F R

Symmetric: If m ∠ A equal m ∠ B, then m ∠ B Equal m ∠ A, If ∠ A congruent ∠ B, then ∠ B congruent ∠ A Transitive: If m ∠ Zequal m ∠ Y and m ∠ Y Equal m ∠ X, then m ∠ Z equal m ∠ X, If ∠ Z congruent ∠ Y and ∠ Y congruent ∠ X, then ∠ Z congruent ∠ X Reflexive: m ∠ T = m ∠ T, ∠ T congruent to ∠ T

m ∠ 1 = m ∠ 2 and m ∠ 2 = m ∠ 3, then m ∠ 1= m ∠ 3 m ∠ 1 = m ∠ 1 m ∠ 1 = m ∠ 2 then m ∠ 2 = m ∠

It is a proving format were you make a t table and put your statements on the left and reasons on the right Examples

Linear pair postulate (LPP): a postulate that states that every linear pair angles are supplements

Congruent complements theorem: if two angles are complements of the same angle, then the two angles are congruent Congruent Supplements theorem: If two angles are supplementary to the same angle then they are congruent.

If I say that <1 and <2 are complementary then <2 and <3 are complementary. Therefore <1 must be congruent to <3. m<R + m<S = 90 degrees and m<S + m<T = 90 degrees, So <R and <T are congruent. M<1= is a third of right angle M<2=is two thirds of a right angle degrees M<3= is one third of a right angle <1 and<2 are complements and <2 and <3 are complements then <1 is congruent or equal to <3

<C + <D = 180 degrees and m<D + m<E = 180 degrees. < C and <E are equal or congruent. <A = 120 degrees <B=50 degrees <a=120 degrees <A and <C are equal or congruent. If <T and <R are supplementary then <R and <S are supplementary. We conclude <T is equal or congruent to <S.

Vertical angle theorem (VAP): This theorem states that vertical angles are congruent to is opposite (they add up to 360 degrees Opposite If one of the angles measure 90 degrees then all of them will measure 90 degrees

This theorem states that: if points A, B, C, and D are all collinear, then segment AB is congruent to segment CD then segment AC is congruent to segment BD.

If from Mercury to Venus is the same as from Earth to Mars, then from Mercury to Earth is the same as from Venus to Mars. If from CAG to Karl's house is the same as from my house to hyperpiaz then form Karl's to hyprpaiz is the same as from my house to CAG. If from my room to my sister’s room is the same as from my parent’s room to my brother’s room, then from my sister’s to my parent's is the same as from my brother's to mine.