Section 5.4 Review Inverse and Contrapositive Click your way through this lesson

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Presentation transcript:

Section 5.4 Review Inverse and Contrapositive *Click your way through this lesson*

Objective State Standard G.1.D To write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

Negation

Salem is the capitol of Washington State False Negation

Salem is not the Capitol of Washington State True Negation Negation

What is the negation of these statements? 1. ∆ABC is a right triangle. 2. <ABC is an acute angle. 3. Lines m and n are perpendicular. 4. Lines q and r are not parallel. Negation

What is the negation of these statements? 1. ∆ABC is NOT a right triangle. 2. <ABC is NOT an acute angle. 3. Lines m and n are NOT perpendicular. 4. Lines q and r ARE parallel. Negation

Inverse Conditional: If A, then B. Inverse: If not A, then not B.

Inverse

Conditional: If a figure is a square, then it is a rectangle. True?.... Yes Inverse Square: a four sided figure with all sides congruent and all angles congruent. Rectangle: a four sided figure with all angles congruent.

Inverse Square: a four sided figure with all sides congruent and all angles congruent. Rectangle: a four sided figure with all angles congruent. Inverse: If a figure is not a square then it is not a rectangle. True?.... No

Inverse: If a figure is not a square then it is not a rectangle. False Conditional: If a figure is a square, then it is a rectangle. True Inverse

Conditional Statement: If A, then B. Converse Statement: If B, then A. Inverse Statement: If not A, then not B. No Guarantee. Just because the Conditional is true that the Converse or Inverse are true. Inverse

Conditional Statement: If you are a sailor, then you can swim. Inverse True False Converse Statement: If you can swim, then you are a sailor. Inverse Statement: If you are not a sailor, then you cannot swim.

Contrapositive

Conditional: If A, then B. Inverse: If not A, then not B. Contrapositive If not B, then not A.

Contrapositive If you are a sailor, then you can swim. If you cannot swim, then you are not a sailor. True

Contrapositive Conditional: If A, then B. Inverse: If not A, then not B. Contrapositive If not B, then not A. Not necessarily true Always true

Check Your Understanding Write the converse, inverse and contrapositive of this statement: “If you run everyday, then you will get in shape.”

Check Your Understanding “If you run everyday, then you will get in shape.” Converse Inverse Contrapositive If you get in shape, then you run everyday. If you don’t run everyday, then you will not get in shape. If you don’t get in shape, then you did not run everyday.

What you Should Know Be able to recognize: Conditional Converse Inverse Contrapositive

What you Should Know If you are still confused or would like more information, check out this video.video

Assignment Pg 283, 1-19 odd and # 22

References How to draw navy ships in 8 steps. [Web]. Retrieved from to-draw-navy-ships.htm Jsovick. (Producer). (2011). G1d converse, inverse, and contrapositive. [Web]. Retrieved from ADUO08