Download - Given Points D = (4,5) E = (8,11) X = (6, 8) Write as many conjectures as you can Starter
Given PointsD = (4,5)E = (8,11)X = (6, 8)
Write as many conjectures as you can
Starter
Geometry
Chapter 2 section 2The
Conditional Statement
Conditional Statement
A statement in the form If(a condition), then (a second condition)
If Dave takes an aspirin then he can walk without a limp
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)
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 1800
• Non-collinear points cannot be between A and B
• Snoozels love to kingklip
Parts of an If Then Statement
If It is an orange then it is a fruit
Hypothesis Conclusion
Hypothesis:
Conclusion:
Find the Hypothesis and the Conclusion
1. If I eat onions then I get sick2. If it’s a dogit’s sunny on TuesdaysBill likes dogsBirds can flyPeople do not like to be told what to do
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
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
Converse:
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)
Negation:
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
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
Inverse:
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
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
Contrapositive:
Truth?
• If a statement is true
• Is the converse true?• Is the inverse true?• Is the contrapositive true?
Do Now!
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Problems 6 – 17 & 19 – 49 odd57 – 67 all