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