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Geometry

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Geometry

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    1. Geometry Chapter 2: Logic and Reasoning

    2. 2.2 If-Then Statements and Postulates

    3. Vocabulary If-then statements Conditional Statements hypothesis conclusion converse negation inverse contrapositive Postulate

    4. Vocabulary: If-then statements: if ______ then _____. Conditional statements: if ______ then _____.

    5. Vocabulary Hypothesis (given) If ____ then ______.

    6. Topic 1: IF-Then Statement If-Then Statements: A statement in If-Then form Often called Conditional statement If part is called the hypothesis The if part is often given the variable p The if part is always the GIVEN in reasoning Then part is called the conclusion The then part is given the variable q The then part is always the CONJECTURE or PROVE in reasoning In Words: If p then q In Symbols: p ? q Re-writing a statement in if-then form. Ask yourself two questions: What are we talking about? (this is the If) What about it? (this is the then)

    7. Examples Identify the hypothesis and the conclusion If it is raining then it is cloudy. Write the statement in if- then form Adjacent angles have a common side What are we talking about? Adjacent angles What about it? They have a common side If angles are adjacent then they have a common side

    8. Vocabulary Negation: To say something is NOT Example: It is raining. Negation: It is not raining Symbol: ~

    9. Re-writing in If-Then Statement Re-writing a statement in if-then form. Ask yourself two questions: What are we talking about? (this is the If) What about it? (this is the then) Example: Vertical Angles are congruent What are we talking about? What about it?

    10. Example Write the inverse, converse and contrapositive of the statement: vertical angles are congruent. Then determine if the statement is true. Inverse: Converse: Contrapositive:

    11. Example part 1 vertical angles are congruent. If: Then: Inverse: Converse: Contrapositive:

    12. Example part 2

    13. You Try

    14. You try Write the inverse, converse and contrapositive of the statement: a line contains at least two points. Then determine if the statement is true: Inverse: Converse: Contrapositive:

    15. Example Write the inverse of the conditional Vertical angles are congruent. Determine if the inverse is true or false. If false, give a counter-example. Statement: If (what are we talking about) then (what about it) If angles are vertical then they are congruent Inverse (~p?~q) If angles are not vertical then they are not congruent FALSE Write the contrapostive of the statement a line contains at least two points. Determine if the contrapositive is true or false. If false, give a counter-example. Statement If (what are we talking about) then (what about it) If it is a line then it contains at least two points Contrapositive (~q?~p) If it does not contain at least two points then it is not a line FALSE

    16. Vocabulary Postulate: Rules that cannot be proven for sure—no counterexample has been found Through any two points there is exactly one line

    17. Vocabulary Postulate: Rules that cannot be proven for sure—no counterexample has been found

    18. Homework Page 81; 28, 36

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