_(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples. _(0-10 pts)

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Presentation transcript:

___(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples. ___(0-10 pts) Describe what a counter-example is. Give at least 3 examples. ___(0-10 pts) Describe what a definition is. Give at least 3 examples. ___(0-10 pts) Describe what a bi-conditional statement is. How are they used? Why are they important? Give at least 3 examples. ___(0-10 pts) Describe what deductive reasoning is and how it is used. Include a discussion about symbolic notation and how it works. Give at least 3 examples. ___(0-10 pts) Describe the laws of logic. Give at least 3 examples of each. ___(0-10 pts) Describe how to do and algebraic proof using the algebraic properties of equality. Give at least 3 examples. ___(0-10 pts) Describe the segment and angle properties of equality and congruence. Give at least 3 examples. ___(0-10 pts) Describe how to write a two-column proof. Give at least 3 examples. ___(0-10 pts) Describe the linear pair postulate. Give at least 3 examples. ___(0-10 pts) Describe the congruent complements and supplements theorems. Give at least 3 examples of each. ___(0-10 pts) Describe the vertical angles theorem. Give at least 3 examples. ___(0-10 pts) Describe the common segments theorem. Give at least 3 examples.

A Conditional statement is when Q is true then p is true also. In other words if the hypothesis is true then the conclusion is true. If Q  P. If you finish your homework, you may play outside. If you help me with the work, I will pay you some money. If you clean the dog´s cage, then you may go to sleep.

Counterexamples are examples that show that the hypothesis is wrong. You just need 1 to prove it is not true. If you jump the ramp, you will die. It is not true because you can land ok. If you dont do your HW now you will get a 0. Not true because you can do it in the bus. If you don´t watch tv, you wont finish your chores. No because you can stop watching in few minutes.

Definitions are the adjectives or reasons that describe why something is that way or what something is. Fire is a reaction that has to do with energy. Tennis is a sport where a racket is used. A t.v. attracts diferent types of sygnals.

The Biconditional statement is known as, If and only If. In a shorter way you write it as Iff. This says that P if and only if Q. This is like a law because it will only give the same answer all the time. You go outside iff you do your homework. I will go to the movies iff it is Friday. I will eat in Mc donalds iff I have soccer practice.

The deductive reasoning is when you prove something by logic or observations. This is not that same as inductive meaning that you prove something by facts. All ipod touch are touch so that means that any ipod that is touch is an ipod touch Any animal that has fur is a mamal so every mamal has fur. Every period is 75 minutes long, therefor if you are in a perdiod then it is 75 minutes.

There are 2 laws. The Law of Detachment that says that if p then q. P is true so then Q is true also. Every Friday I go to the movies. Today I went to the movies so today is Friday. Every Monday I go to the gym. Today i am in the gym so today is Monday. Not even 1 mamal puts eggs. The animal I am looking layed an egg so it is not a mamal.

The other law is called the law of syllogism. This law says that if P then Q and if Q then R all are true. That means that P then R is true too. Today is Monday. I am in the market. Every Monday I go to the market so If im in the market then it is monday. If an animal eats bananas then its a monkey. There is an animal eating bananas so it is a monkey. If you have a long hair then they will cut it. They are cutting your hair so that means you have it long.

The linear pair postulate say that if 2 lines form 180 degrees then they are supplementary.

They are a series of steps used to prove each step you do to prove the given. Additive Substraction Multiplication Division And so…

A way to prove a statement with a reason. It is an organized and fast way to prove the given and what you have to prove. /SOUquUJShJI/AAAAAAAAATA/aLgWr Md6o3A/s400/3.3b.bmp

The complementary (congruent) theorem states that if 2 ANGLES are congruent and form a right angle then they both have the same measure, 90 degrees.

Supplementary has the same rule as before with complementary. Just the measure changes to the double which is 360 degrees,

This theorem states that the opposite angles in a 360 angle are coungruent so they have the same measure. The other 2 vertical angles are also congruent.

This theorem states that if ab is coungruent to cd then ac is congruent also to bd. This is used in segments. My bathroom to my bedroom is the same distance to my moms room and her bathroom so that means that my bathroom and my moms bathroom is the same distance from my bedroom to her bedroom. DE is the same distance from FG so DF is same distance compared to segment EG. My dogs cage and my cats cage has the same distance to my birds and snake cage. So my dogs and birds is same distance to cats and snakes cage