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Chapter 2

Chapter 2. Section 2.1 Conditional Statements. Conditional Statement. Type of logical statement 2 parts Hypothesis/Conclusion Usually written in “if-then” form If George goes to the market , then he will buy milk. Hypothesis. Conclusion.

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Chapter 2

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  1. Chapter 2 Section 2.1 Conditional Statements

  2. Conditional Statement • Type of logical statement • 2 parts • Hypothesis/Conclusion • Usually written in “if-then” form • If George goes to the market, then he will buy milk. Hypothesis Conclusion If the hypothesis is true then the conclusion must be true

  3. Rewrite each conditional statement in if-then form • It is time for dinner if it is 6 pm. • If it is 6 pm, then it is time for dinner • There are 12 eggs if the carton is full • If the egg carton is full, then there are 12 eggs. • A number is divisible by 6 if it is divisible by 2 and 3. • If a number is divisible by 2 and 3, then it is divisible by 6 • An obtuse angle is an agle that measures more than 90 and less than 180. • If an angle is obtuse then it measures more than 90 and less than 180. • All students taking geometry have math during an even numbered block • If you are taking geometry, then you have math during an even numbered block.

  4. Counter Example • Used to prove a conditional statement is false • Must show an instance where the hypothesis is true and the conclusion is false. • Ex. If x2 = 9 then x = 3 • Counter Ex. (-3)2 = 9, but –3,  3 • Only need one counter example to prove something is not always true.

  5. Decide whether the statement is true or false. If it is false, give a counter example • The equation 4x – 3 = 12 + 2x has exactly one solution • True • If x2 = 36 then x = 18 or x = -18 • False: (6)2 = 36 and 6  18 or 6  -18 • Thanksgiving is celebrated on a Thursday • True • If you’ve visited Springfield, then you’ve been to Illinois. • False: If you’ve visited Springfield, then you’ve been to Massachusetts (Springfield MA.) • Two lines intersect in at most one point. • True

  6. New statements formed from a conditional • Converse: Switch the hypothesis and conclusion • Conditional: If you see lightning, then you hear thunder • Converse: If you hear thunder, then you see lightning • If you like hockey, then you go to the hockey game • If you go to the hockey game, then you like hockey • If x is odd, then 3x is odd • If 3x is odd, then x is odd • If mP = 90, then P is a right angle • If P is a right angle, then mP = 90

  7. New statements formed from a conditional • Inverse: When you negate the hypothesis and conclusion of a conditional • Negate: To write the negative of a statement • Conditional: If you see lightning, then you hear thunder • Inverse: If you do not see lightning, then you do not hear thunder • If you like hockey, then you go to the hockey game • If you don’t like hockey, then you don’t go to the hockey game • If x is odd, then 3x is odd • If x is not odd, then 3x is not odd • If mP = 90, then P is a right angle • If mP  90, then P is not a right angle

  8. New statements formed from a conditional • Contrapositive: When you switch and negate the hypothesis and conclusion of a conditional • Conditional: If you see lightning, then you hear thunder • Contrapositive: If you do not hear thunder, then you do not see lightning • If you like hockey, then you go to the hockey game • If you don’t go to the hockey game, then you don’t like hockey • If x is odd, then 3x is odd • If 3x is not odd, then x is not odd • If mP = 90, then P is a right angle • If P is not a right angle, then mP  90

  9. Equivalent Statements • When two statements are both true, they are called equivalent statements

  10. Point, Line, and Plane Postulates • Through any two points there exists exactly one line • A line contains at least two points • If two lines intersect, then their intersection is exactly one point (14) • Through any three noncollinear points there exists exactly one one plane

  11. Point, Line, and Plane Postulates • A plane contains at least three noncollinear points • If two points lie in a plane, then the line containing them lies in the same plane (15) • If two planes intersect the, then their intersection is a line. (16)

  12. Use the diagram to state the postulate that verifies the statement • The points E, F, and H lie in a plane • Postulate #8: Through any three noncollinear points there exists one plane. • The points E and F lie on a line • Postulate #5: Through any two points there exists exactly one line

  13. Use the diagram to state the postulate that verifies the statement • The planes Q and R intersect in a line • Postulate #11 If two planes intersect the, then their intersection is a line. • The points E and F lie in plane R. Therefore, line m lies in plane R • Postulate #10: If two points lie in a plane, then the line containing them lies in the same plane

  14. HW #15Pg 75-78 10-50 Even, 51, 55, 56 

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