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Given Points D = (4,5) E = (8,11) X = (6, 8) Write as many conjectures as you can Starter

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Geometry Chapter 2 section 2 The Conditional Statement

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A statement in the form If(a condition), then (a second condition) If Dave takes an aspirin then he can walk without a limp

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Formal Logic Conditional statements are important in Formal Logical Structures All carrots are tubers (Normal English) If it’s a carrot then it’s a tuber (Formal Logic)

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Put the following into If Then Fire engines are red Telephone poles are not orange No dogs can go into the theater Angles are less than 180 0 Non-collinear points cannot be between A and B Snoozels love to kingklip

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Parts of an If Then Statement If It is an orange then it is a fruit Hypothesis Conclusion

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Hypothesis: Conclusion:

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Find the Hypothesis and the Conclusion 1. If I eat onions then I get sick 2.If it’s a dog it’s sunny on Tuesdays Bill likes dogs Birds can fly People do not like to be told what to do

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Converse Every conditional statement has a converse Statement: If it’s yellow then it’s a banana Converse: If it’s a banana then it’s yellow

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Converse Statement: If B is between A and C then AB& C are collinear Converse: If AB& C are collinear then B is between A and C

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Converse:

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Negation Statement: Carl is a Firefighter Negation: Carl is not a fire Fighter Statement: Angle G is Acute Negation: Angle G is not Acute (angle G is right or obtuse)

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Negation:

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Inverse Every conditional statement has a inverse Statement: If it’s yellow then it’s a banana Converse: If it’s not yellow then it’s not a banana

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Inverse Statement: If B is between A and C then AB& C are collinear Converse: If B is not between A and C then AB& C are not collinear

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Inverse:

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Contrapositive Every conditional statement has a contrapositive Statement: If it’s yellow then it’s a banana Converse: If it’s not a banana then it’s not yellow

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Contrapositive Statement: If B is between A and C then AB& C are collinear Converse: If AB& C are not collinear then B is not between A and C

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Contrapositive:

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Truth? If a statement is true Is the converse true? Is the inverse true? Is the contrapositive true?

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Do Now! Page 80 – 83 Problems 6 – 17 & 19 – 49 odd 57 – 67 all

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Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3.

Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3.

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