Chapter 2

1 / 14

# Chapter 2 - PowerPoint PPT Presentation

Chapter 2. Section 2.1 Conditional Statements. Conditional Statement. Type of logical statement 2 parts Hypothesis/Conclusion Usually written in “if-then” form If George goes to the market , then he will buy milk. Hypothesis. Conclusion.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Chapter 2' - Sophia

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Chapter 2

Section 2.1

Conditional Statements

Conditional Statement
• Type of logical statement
• 2 parts
• Hypothesis/Conclusion
• Usually written in “if-then” form
• If George goes to the market, then he will buy milk.

Hypothesis

Conclusion

If the hypothesis is true then the conclusion must be true

Rewrite each conditional statement in if-then form
• It is time for dinner if it is 6 pm.
• If it is 6 pm, then it is time for dinner
• There are 12 eggs if the carton is full
• If the egg carton is full, then there are 12 eggs.
• A number is divisible by 6 if it is divisible by 2 and 3.
• If a number is divisible by 2 and 3, then it is divisible by 6
• An obtuse angle is an agle that measures more than 90 and less than 180.
• If an angle is obtuse then it measures more than 90 and less than 180.
• All students taking geometry have math during an even numbered block
• If you are taking geometry, then you have math during an even numbered block.
Counter Example
• Used to prove a conditional statement is false
• Must show an instance where the hypothesis is true and the conclusion is false.
• Ex. If x2 = 9 then x = 3
• Counter Ex. (-3)2 = 9, but –3,  3
• Only need one counter example to prove something is not always true.
Decide whether the statement is true or false. If it is false, give a counter example
• The equation 4x – 3 = 12 + 2x has exactly one solution
• True
• If x2 = 36 then x = 18 or x = -18
• False: (6)2 = 36 and 6  18 or 6  -18
• Thanksgiving is celebrated on a Thursday
• True
• If you’ve visited Springfield, then you’ve been to Illinois.
• False: If you’ve visited Springfield, then you’ve been to Massachusetts (Springfield MA.)
• Two lines intersect in at most one point.
• True
New statements formed from a conditional
• Converse: Switch the hypothesis and conclusion
• Conditional: If you see lightning, then you hear thunder
• Converse: If you hear thunder, then you see lightning
• If you like hockey, then you go to the hockey game
• If you go to the hockey game, then you like hockey
• If x is odd, then 3x is odd
• If 3x is odd, then x is odd
• If mP = 90, then P is a right angle
• If P is a right angle, then mP = 90
New statements formed from a conditional
• Inverse: When you negate the hypothesis and conclusion of a conditional
• Negate: To write the negative of a statement
• Conditional: If you see lightning, then you hear thunder
• Inverse: If you do not see lightning, then you do not hear thunder
• If you like hockey, then you go to the hockey game
• If you don’t like hockey, then you don’t go to the hockey game
• If x is odd, then 3x is odd
• If x is not odd, then 3x is not odd
• If mP = 90, then P is a right angle
• If mP  90, then P is not a right angle
New statements formed from a conditional
• Contrapositive: When you switch and negate the hypothesis and conclusion of a conditional
• Conditional: If you see lightning, then you hear thunder
• Contrapositive: If you do not hear thunder, then you do not see lightning
• If you like hockey, then you go to the hockey game
• If you don’t go to the hockey game, then you don’t like hockey
• If x is odd, then 3x is odd
• If 3x is not odd, then x is not odd
• If mP = 90, then P is a right angle
• If P is not a right angle, then mP  90
Equivalent Statements
• When two statements are both true, they are called equivalent statements
Point, Line, and Plane Postulates
• Through any two points there exists exactly one line
• A line contains at least two points
• If two lines intersect, then their intersection is exactly one point (14)
• Through any three noncollinear points there exists exactly one one plane
Point, Line, and Plane Postulates
• A plane contains at least three noncollinear points
• If two points lie in a plane, then the line containing them lies in the same plane (15)
• If two planes intersect the, then their intersection is a line. (16)
• The points E, F, and H lie in a plane
• Postulate #8: Through any three noncollinear points there exists one plane.
• The points E and F lie on a line
• Postulate #5: Through any two points there exists exactly one line
• The planes Q and R intersect in a line
• Postulate #11 If two planes intersect the, then their intersection is a line.
• The points E and F lie in plane R. Therefore, line m lies in plane R
• Postulate #10: If two points lie in a plane, then the line containing them lies in the same plane