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Analyzing conditional statements

Vocabulary . A conditional statement. is a logical statement that has two parts, a hypothesis and a conclusion.. When a conditional statement is written . in if-then formSymbolic Form. the if" part contains the hypothesis and the then" part contains the conclusion.p?q where

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Analyzing conditional statements

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    1. Analyzing conditional statements Lesson 2.2

    2. Vocabulary A conditional statement

    3. When a conditional statement is written in if-then form Symbolic Form the “if” part contains the hypothesis and the “then” part contains the conclusion. p?q where p is the hypothesis and q is the conclusion

    4. The negation of a statement To write the converse of a conditional statement is the opposite of the original statement. Symbol ~ , switch the hypothesis and conclusion. Symbloic form q ?p  

    5. To write the inverse of a conditional statement,   To write the contrapositive of a conditional statement, negate both the hypothesis and conclusion. Symbolic form ~p?~q first write the converse and then negate both the hypothesis and the conclusion. Symbolic form ~q ? ~p

    6. Practice with the teacher: Example 1: If two lines intersect, then they intersect in exactly one point. Identify the hypothesis and conclusion hypothesis: two lines intersect conclusion: they intersect in exactly 1 point

    7. Example 2 Write this statement as a conditional statement:   A perpendicular bisector is perpendicular to and bisects a segment If a line is perpendicular bisector, then it is perpendicular and bisects the segment.

    8. True statement: If I am an only child, then I have no brothers or sisters.     The negation of a true statement is always false.   The negation of the statement: If I am not an only child, then I have no brothers or sisters

    9. False statement: If I am an only child, then I have brothers or sisters.   The negation of the statement:   The negation of a false statement is always true. If I am not an only child, then I have brothers or sisters.

    10. p is statement ~p is the negation of the statement Try this in pairs: Write ~p tell if each pair is true or false P = Two points determine a unique line. ~p =Two points do not determine a unique line ( False)

    11. P: 2 ˇ 7 = 9 P: Acute angles measure 90 or more. ~ p : 2ˇ 7? 9 ( True) ~p :Acute angles do not measure 90 or more ( True)

    12. P: Supplementary angles have a sum of the 180. P: Linear pairs are complementary. P: Vertical angles are supplementary. ~p: Supplementary angles do not have a sum of 180. ( False) ~p : Linear pairs are not complementary. ( True) ~p: Vertical angles are not supplementary. ( True)

    13.   If a statement is false, all you need is one counterexample to show that it is false.

    14. Is this statement true or false? If it is false, show a counterexample If three points are in a plane, then there is exactly one line that contains those points.   False:

    15. Write the if-then form, the converse, the inverse, and the contrapositive of the statement “Basketball players are athletes.” Decide whether each statement is true or false. If-then form If you are a basketball player, then you are an athlete.  True, basketball players are athletes. Converse If you are an athlete, then you are a basketball player. False, not all athletes play basketball.   Inverse If you are not a basketball player, then you are not an athlete. False, even if you don’t play basketball, you can still be an athlete.   Contrapositive If you are not an athlete, then you are not a basketball player. True, a person who is not an athlete cannot be a basketball player.

    16. Write the if-then form, the converse, the inverse, and the contrapositive of the statement. Decide whether each statement is true or false. All 180° angles are straight angles. All cats are mammals.

    17. Vocabulary: equivalent statements   perpendicular lines.   A biconditional statement   Are when two statements are both true or are both false, they are called two lines that intersect to form a right angle. Symbol is a statement that contains the phrase “if and only if.” Symblic form p?q

    18. Write what you see from this picture using your definitions

    19. A biconditional can only be written if the conditional and the converse of the statement are both true.

    20. Write the definition of supplementary angles as a biconditional. Solution Definition If two angles are supplementary angles, then the sum of their measures is 180°. Converse If the sum of the measures of two angles is 180°, then they are supplementary angles.   Biconditional Two angles are supplementary angles if and only if the sum of their measures is 180°.

    21. Summary: Looking over the today’s work. What are the major key points we have made.

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