Geo Journal #2

Maricarmen HernandezGeo Journal #2Conditional If-Then Statements:A conditional if-then statement is when a sentence has a hypothesis (if) and a conclusion (then). If is shown by P, and then is shown by Q.

If I eat my vegetables, then Ill be strong.(P) (Q)Conditional If-Then Statements example:If I eat my vegetables, then Ill be strong.(P) (Q)

Converse- When we switch the hypothesis and the conclusion of a conditional statement. QPIf Im strong, then I ate my vegetables.

Inverse- Same as conditional but hypothesis & conclusion are NOT.If I didnt eat my vegetables, then Im not strong.

Contrapositive- Negative the converse.If Im not strong, then I didnt eat my vegetables.

Counter-examples:

When an example is used to disprove a hypothesis. Mammals dont lay eggs.The platypus does. All water animals arent mammals.Dolphins are mammals. When you add, the result is always positive.-7 + 3 = -4Definition:A definition is a biconditional statement that defines what something is.A number is prime if it can only be divided by one and itself.Its a statement if the line has a start and an end.Its a triangle if it has 3 sides.Bi-conditional Statements:Its when both the conditional and the converse statements are true. If and only if (iff). They are used to show when both the conclusion and the hypothesis depend of each other and both are true.They are important because we use it in an every day basis, either consciously or unconsciously. We use it for logic and in proofs.

Examples:A shape is a triangle iff it has 3 sides.A line iff it goes on forever on both directions.A ipod iff its designed by Apple and produces music.Deductive Reasoning:A way of reasoning in which you use data and logic to make conclusions.Collect DataLook at the FactsUse logic make the conclusion.Ex)Research shows that 5 of 10 kids in the class have blue pens, so we can say 50 out 100 kids in the grade have blue pens.Research shows that 1 out of every 2 kids in our grade have cell phones, so we can say that half the grade have cell phones.Research says that one of every 3 kids in CAG have crocs, so we can say that in a class of 21, 7 kids own crocs.Symbolic Notation:When a symbol is used instead of the word/words.Ex) times: x, equal: =7Laws of logic:Law of detachmentLaw of syllogism

Law of Detachment: If PQ and P is true, then Q must be too.Ex1) You must be at least a meter and a half tall to ride the rollercoaster. Sandra is 1.20 meters tall. Sandra cant ride the rollercoaster.Ex2) If you are over 10 years old, you must pay full price to enter the park. Sean is 13 years old. Sean will pay full price.Ex3) You need at least 65% in a class to pass the grade. Tawnys grade is 50%. Tawny did not pass the grade.

Law of Syllogism:If PQ and QR are true, then PR is true.

Ex1) If you live in Guatemala city, then you live in Guatemala. If you live in Guatemala, then you live in Central America. I live in Guatemala city, therefore I live in Central America.Ex2) If you have Geometry, then you are in high school. If you are in high school, you have more than 13 years old. Ron is in Algebra, so he has more than 13 years.Ex3) If you have a car, then you can drive. If you can drive, you have a license. Cedric has a car, so he has a license.Algebraic Proofs & Properties:

Addition Property If a=b, then a+b=c Subtraction Property If a=b, then a c is b cMultiplication Property If a=b, then ac=bc Division Property If a=b & c dont equal zero, then a/c = b/c Reflexive Property a=a Symmetric Property If a=b then b=a Transitive Property if a=b and b=c, then a=c Substitution If a=b, then b can be replaced by a in any situation

Step by step arguments that prove something.StatementReasonEx1) 4x-2=6x+84x-2=6x+8 +2 +24x=6x+10-6x -6x-2x=10-2 -2X=-5GivenAdditionSimplifySubtractionSimplifyDivisionSimplifyQ.E.DStatementReasonEx2) x+8=9X+8=9 -8 -8X=1GivenSubtractionSimplifyQ.E.DStatementReasonEx3) 3x-8=193x-8=19 +8 +83x=273 3x=7GivenAdditionSimplifyDivisionSimplifyQ.E.DProperties of congruency and equality:

Transitive: If AB=CD, and CD=EF, then AB=EF Symmetric: If AB = CD, then CD=AB. Reflexive: : AB= AB, ABcongruent to AB 2 Column ProofIts a way to prove something in a chart, you put the statement in the left and the reason in the right. Write down important information Draw a picture Mark what's given.Write down the info and pictures. GO FOR IT!!!StatementReasonEx1) Given: LPP-if 2 angles for a linear pair then they are supplementary.