Conditional Statements

1
Chapter 2

• Section 2.1
• Conditional Statements

2
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
3
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.

4
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.

5
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 youve visited Springfield, then youve been
  to Illinois.
• False If youve visited Springfield, then youve
  been to Massachusetts (Springfield MA.)
• Two lines intersect in at most one point.
• True

6
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

7
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 dont like hockey, then you dont 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

8
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 dont go to the hockey game, then you
  dont 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

9
Equivalent Statements

• When two statements are both true, they are
  called equivalent statements

Original If m?A 30, then ?A is acute
Inverse If m?A ? 30, then ?A is not acute
Converse If ?A is acute, then m?A 30
Contrapositive If ?A is not acute, then m?A ? 30
10
Point, Line, and Plane Postulates

1. Through any two points there exists exactly one
   line
2. A line contains at least two points
3. If two lines intersect, then their intersection
   is exactly one point (14)
4. Through any three noncollinear points there
   exists exactly one one plane

11
Point, Line, and Plane Postulates

1. A plane contains at least three noncollinear
   points
2. If two points lie in a plane, then the line
   containing them lies in the same plane (15)
3. If two planes intersect the, then their
   intersection is a line. (16)

12
Use the diagram to state the postulate that
verifies the statement

• 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

13
Use the diagram to state the postulate that
verifies the statement

• 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

14
HW 15Pg 75-78 10-50 Even, 51, 55, 56