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2.2 If - Then Statements

2.2 If - Then Statements. OBJ: (1)To Write Statements in If-Then Form (2)To Write Converse, Inverse, & Contrapositive of Statements (3)To ID & Use Basic Postulates About Pts, Lines & Planes. P. Q. The statement. If - then statements. If - then statements are conditional statements.

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2.2 If - Then Statements

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  1. 2.2 If - Then Statements OBJ: (1)To Write Statements in If-Then Form (2)To Write Converse, Inverse, & Contrapositive of Statements (3)To ID & Use Basic Postulates About Pts, Lines & Planes

  2. P Q The statement If - then statements If - then statements are conditional statements If (hypothesis), then (conclusion) Hypothesis--- AKA "P" Conclusion--AKA "Q" Says If P, then Q or P implies Q

  3. Hypothesis:an angle measures 40o Conclusion: it is acute Example: An angle of 40o is acute. Put in If- then form. Identify the hypothesis and the conclusion. If - then form: If an angle measures 40o, then it is acute.

  4. Your Turn: All triangles have 3 sides. Write in If - then form and identify the hypothesis and conclusion If a figure is a triangle, then it has 3 sides. Hypothesis: a figure is a triangle Conclusion: it has 3 sides.

  5. Converse: Change the hypothesis w/ the conclusion. Example: Adjacent angles have a common side. Change to if - then form If 2 angles are adjacent, then they have a common side. Switch the hypothesis w/ the conclusion If 2 angles have a common side, then they are adjacent.

  6. Biconditional Statements • When a conditional statement and its converse are both true. • We can write it as a single statement • Use the phrase if and only if • Abbreviated with iff • Example: If two lines intersect to form a right angle, then they are perpendicular • If two lines are perpendicular, then they intersect to form a right angle • Two lines are perpendicular if and only if they intersect to form a right angle

  7. B False, D Both angles have a common side, but they are not adjacent because they share interior pts. A C Example Continued If 2 angles have a common side, then they are adjacent. Is the converse true or false? If false, provide a counterexample.

  8. Your Turn: Write the converse of the true conditional An angle that measures 120o is obtuse. Determine if the converse is true or false. If false, give a counter example. Converse: If angle is obtuse, then it measures 120o . False, because the angle could measure anything > 90o .

  9. Negation Denial of a statement. Example: an angle is obtuse --> an angle is not obtuse The key to negation is to understand that it is opposite of the original statement. In the example, if the statement is true, then the negation is false. If the statement is false, then the negation is true.

  10. Inverse: Original statement: P --> Q If P, then Q If you are in math class then you are in Mr. Chandler's class. Inverse statement: not P --> not Q if not P then not Q If you are not in math class then you are not in Mr. Chandler's class.

  11. Contrapositive: Original statement: p --> Q If p then Q If you are in math class then you are in Mr. Chandler's class Contrapositive: not Q --> not P If not Q then not P If you are not in Mr. Chandler's class, then you are not in math class.

  12. Summary Original: P  Q Inverse: not P  not Q Converse: Q  P Contrapositive: not Q not P

  13. What you need to be able to do: • Be able to convert statements to if - then format • Memorize the 4 if then statement formats • provide counterexamples if statements are false

  14. Postulates • Principle accepted as true w/o proof • 2 pts determine a line • Through 3 nonlinear pts, there is exactly 1 plane • Lines contain at least 2 pts

  15. Postulates Continued • A plane contains at least 3 pts not on the same line • if 2 pts lie in a plane, then the line containing the 2 pts lies in the plane • If 2 planes intersect, the intersection is a line

  16. Homework: • Put this in your agenda • pg 82 1 – 29 odd, 50 - 52

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