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::::::::JOURNAL 5 GEOMETRY ::::::::

::::::::JOURNAL 5 GEOMETRY ::::::::. Hyungum Kim 9-4. Describe what a conditional if-then statement and the different parts of a conditional statement . Give at least 3 examples. The statement that is divided in two parts: hypothesis and conclusion.

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::::::::JOURNAL 5 GEOMETRY ::::::::

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  1. ::::::::JOURNAL 5 GEOMETRY :::::::: Hyungum Kim 9-4

  2. Describe what a conditional if-then statement and the different parts of a conditionalstatement. Give at least 3 examples. • The statement that is divided in two parts: hypothesis and conclusion. • Contra positive, inverse of statement, converse. • Examples: • If I get good grades then I will go outside. • If I do my homework then I will go to the party. • If I start to drink milk then I will grow.

  3. Describe what a counter-example is. Give at least 3 examples. • In other words it’s the inductive reasoning. It’s against theorem, hypothesis and proposition. • Examples: -All students are blonde : some are brunet. -All computers are hp: there are mac. -Everyone has a white jersey: Some don’t.

  4. Describe what a definition is. Give at least 3 examples. • First of all every definition is bi-conditional and they define something in any way. • Examples: • Eraser: Removes something that was in pencil or a whiteboard marker. • Pencil: Erasable type of tool to write or draw. • Bed: Comfort place to sleep or rest.

  5. Describe what a bi-conditional statement is. How are they used? Why are they important? Give at least 3 examples. • When the conditional and converse are both true.Represented in iff(if and only if) • It is important to use because it’s a less complex way to write both. • It is used in iff • Examples: • I’ll wear clothes iff I go outside. • I’ll answer the phone iff it is ringing. • Tomorrow is n tomorrow if and only if today is today.

  6. 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. • When you make a conclusion with past experiences. • Symbolic notation: describing expressions in a symbolic way so you don’t write it. • Examples: • Sun is the biggest star. So that’s why the other stars look really small. • Being cold makes you get sick. That’s why I got sick during winter. • Water hydrates your body. That’s why I need it after sports.

  7. Describe the laws of logic. Give at least 3 examples of each. • Law of detachment: If P Q is a true statement then if P is true then Q must be true also. • Examples: • If today is Monday then will go to school. Today is Monday you will go to school. • If I get my homework done then I will go to the party. If you get your homework done you will go the party. • If I wake up early then I will not be late for school. If you wake up early you will not be late for school. • Law of Syllogism: If PQ and QR are both true statements then if P is true the R is true. • Example: • If it’s a school day I will go on Monday. • If I get my homework done then I get to go early. • If I wake up early I will be responsible.

  8. Describe how to do and algebraic proof using the algebraic properties of equality. Give at least 3 examples. • A statement or argument used in such a validation. Step by step solving a problem. • Example: • 3x-1=5 given • +1+1 addition • 3x=6 simplification • /3 /3 division • X=2 simplificatioin

  9. Two column proof: given statement 3x-1=5 +1 +1 3x=5 /3 /3 X=2 Given Addition Simplify Division simplify

  10. Describe the segment and angle properties of equality and congruence. Give at least 3 examples. • Division: a=b THEN a/c=b/c • Addition: a=b a+c= b+c • Multiplication: a+b ac= bc • Subtraction: a=b  a-c+ b-c • Transitive: a=b and b=c  a=c • Symmetric: a=b b=a • Reflective: a=a

  11. Describe the linear pair postulate. Give at least 3 examples. • When 2 angles are linear they are linear pair postulate, also known as LPP. ALL ADD UP TO 180 °

  12. Describe the congruent complements and supplements theorems. Give at least 3 examples of each. • When 2 angles are supplementary then they are congruent. T H M K A

  13. Describe the vertical angles theorem. Give at least 3 examples. • Vertical angles are congruent, they are formed in a ㄴ shape. 90°

  14. Describe the common segments theorem. Give at least 3 examples. • When for example 4 points are collinear point 1,2 are congruent to 3,4 so then 2,4 is congruent to 1,3. • Examples: • The distance from the pencil to the eraser is the same distance to sharpener to the paper. So then the eraser-paper is same distance to pencil-sharpener. • A B C D

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