Geo 2.1 condtional statements


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Geometry Section 2.1 on Conditional Statements and the point line and plane postulates.

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  • -Pay attention to how the word “not” acts in this statement- Often you must adjust the tense of the verb or add helping verbs to make the sentence “sound” right without changing the logical structure of the sentence
  • Geo 2.1 condtional statements

    1. 1. Unit 2. Section 2.1CONDITIONAL STATEMENTS
    2. 2. - Conditional statements are used in every field of human endeavor.- They are crucial to the search for truth- If you are going to be able to adequately interpret and judge the statements you hear, you must understand the structure of Conditional statements.-WARNING: Once you get good at these, you may be amused by statements made by politicians and other public speakers.
    3. 3. Objectives Students will be able to:  Identify conditional statements and place them in if-then form  Identify the hypothesis and conclusion of a conditional statement  Convert conditional statements into their other logical variants  Identify and use truth relationships of conditional statements  State and use the point, line and plane postulates of geometry
    4. 4. What is a ConditionalStatement? A statement that can be written in the format: If …., then …. The part after “if” is called the hypothesis  Do not confuse this with the word “hypothesis” from science The rest (after “then”) is the conclusion
    5. 5. Statements Not in If-Then Form- Often statements are not in if –then form, but totest them out scientifically, we must convert them- In English, there are infinite ways to rephrase aconditional statement; however, we will cover thethree most common variations here
    6. 6. Standard Sentence Split the subject and predicate. Add “If it is” or “If they are” to the subject Add “then it” or “then they” to the predicate Smooth out the grammar Example: “All dogs go to heaven.”  “If they are dogs, then they go to heaven.”
    7. 7. “Whenever” or “When” Replace “whenever” or “when” with “if” Add “then” after the comma Example: “Whenever I see a seagull, I think of home.”  If I see a seagull, then I think of home.
    8. 8. “If” at the end Move the “if” clause to the beginning Add “then” after the “if” clause Example: “I eat if I am hungry.”  “If I am hungry, then I eat.”
    9. 9. Logical Variations of theConditional-Often a conditional statement can be difficult toprove or unwieldy to use.- By using logical variations, we find forms easier toprove or use.
    10. 10. Converse, Inverse, &Contrapositive Converse: formed by swapping the hypothesis and the conclusion Inverse: formed by negating the hypothesis and conclusion Contrapositive: formed by both negating and swapping the hypothesis and conclusion
    11. 11. Equivalent Statements If the Conditional is true (or false) then so is the Contrapositive and vice versa. Similarly, if the Converse is true, then so is the Inverse and vice versa If both the Conditional and its Converse are true, then they can be rewritten as a Biconditional statement (more next class)
    12. 12. Example 1 If you added 2+2, you got 4 CONVERSE: If you got 4, then you added 2+2. INVERSE: If you did not add 2+2, you did not get 4. CONTRAPOSITIVE:If you did not get 4, then you did not add 2+2.
    13. 13. Example 2 (the word “not”) If you do not eat, you will be hungry CONVERSE: If you are hungry, then you did not eat. INVERSE: If you ate, then you are not hungry. CONTRAPOSITIVE: If you are not hungry, then you ate.
    14. 14. Point, Line and Plane Postulates
    15. 15. Point, Line & Plane Postulates5. Through any two points there exists exactly one line.6. A line contains at least two points.7. If two lines intersect, then their intersection is exactly one point.8. Through any three noncollinear points there exists exactly one plane.9. A plane contains at least three noncollinear points.10. If two points lie in a plane, then the line containing them lies in the plane.11. If two planes intersect, then their intersection is a line.
    16. 16. Reference McDougal Littell Geometry (2001), Section 2.1