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3.5

3.5. What’s the Condition? Pg. 16 Conditional Statements. 3.5 – What’s the Condition?______________ Conditional Statements.

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3.5

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  1. 3.5 What’s the Condition? Pg. 16 Conditional Statements

  2. 3.5 – What’s the Condition?______________ Conditional Statements Today you are going to explore conditional statements and rearrange them to develop a different meaning. You are also going to examine how to prove something with contradictions and counterexamples.

  3. If ______, then _________ If a, then b Part following “if” a Part following “then” b

  4. 3.24 – PARTS OF CONDITIONAL STATEMENTS Identify the hypothesis and conclusion of each conditional statement. If a # is divisible by 2, then the number is even. If the sidewalks are wet, then it has been raining. conclusion hypothesis conclusion hypothesis

  5. 3.25 – CONDITIONAL STATEMENTS Rewrite the statements in “If …, then….” form. Quadrilaterals with all equal sides are equilateral. If a quadrilateral has all equal sides, then it is equilateral

  6. b. All polygons have three or more sides. If a shape is a polygon, then it has 3 or more sides

  7. 3.26 – COUNTEREXAMPLES If hypothesis happens, then conclusion MUST happen Given hypothesis, conclusion might or might not happen Example the shows statement doesn’t HAVE to happen

  8. you drive a black mustang False, True

  9. obtuse and 130 False, True

  10. Flips the “If” and “Then” If a, then b becomes…. If b, then a

  11. 3.27 – CONVERSES AND TRUE STATEMENTS In the previous problem, you learned that each conditional statement has a converse. Are all converses true? Consider the conditional statement: a. Is this conditional statement true? yes

  12. b. Write the converse of this statement as a conditional statement. Is this converse true? Justify your answer. If , then yes

  13. c. Write the converse of the statement below. Is this converse true? Justify your answer. If , then and corresponding angles False,

  14. 3.28 – CRAZY CONVERSES For each of these problems below, match the statement with the given conditions. Explain your reasoning.

  15. a. A true statement whose converse is true. b. A true statement whose converse is false. c. A false statement whose converse is true. d. A false statement whose converse is false. I. If it is Halloween, then it is October 31st. IV. If you go to Steele Canyon, then your mascot is a cougar III. If you don’t eat steak, then you are a vegetarian II. If you love math, then you love science

  16. Original and converse are true a if and only if b a iff b

  17. 3.29 – BICONDITIONAL STATEMENTS • Rewrite the definition as a biconditional statement. • a. A figure is a square when it is a rectangle with 4 congruent sides A figure is a square iff it is a rectangle with 4 congruent sides

  18. b. Equilateral polygons have all of their sides congruent. A polygon is equilateral iff all of their sides are congruent

  19. Negates the “If” and “Then” If a, then b becomes…. If not a, then not b Negates & flips If a, then b becomes…. If not b, then not a

  20. 3.30 – REWRITING STATEMENTS Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive.

  21. a. A car runs when there is gas in the tank. If-then: ______________________________________ Converse: ______________________________________ Inverse: ______________________________________ Contrapositive: ______________________________________ • If a car runs, then there is gas in the tank • If there is gas in the tank, then the car runs • If the car isn’t running, then there isn’t gas in the tank • If there isn’t gas in the tank, then the car isn’t running

  22. b. All triangles have three sides. If-then: ______________________________________ Converse: ______________________________________ Inverse: ______________________________________ Contrapositive: ______________________________________ • If a shape is a triangle, then it has 3 sides • If a shape has 3 sides, then it is a triangle. • If a shape isn’t a triangle, then it doesn’t have 3 sides • If a shape doesn’t have 3 sides, then it isn’t a triangle

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