Section 5.4 ReviewInverse 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 StateFalse

Negation

Salem is not the Capitol of

Washington State

True

Nega

tion

Nega

tion

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.

•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

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

Contrapositive

•Conditional:If A, then B.

•Inverse:If not A, then not B.

•ContrapositiveIf 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

True

Contrapositive

•Conditional:If A, then B.

•Inverse:If not A, then not B.

•ContrapositiveIf not B, then not A.

Not nece

ssarily

true

Not nece

ssarily

true

Always t

rue

Always t

rue

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

Converse

Inverse

Inverse

Contraposit

ive

Contraposit

ive

•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.

Assignment

•Pg 283, 1-19 odd and # 22

ReferencesHow to draw navy ships in 8 steps.

[Web]. Retrieved from http://tlc.howstuffworks.com/family/how-to-draw-navy-ships.htm

Jsovick. (Producer). (2011). G1d converse, inverse, and contrapositive. [Web]. Retrieved from http://www.youtube.com/watch?v=gvlwsADUO08