Conditional Statements

1
Chapter 2

• Section 2.1
• Conditional Statements

2
Warm-Up

• Name a point collinear with N and U.
• Name a point coplanar with L, M, R.
• Name a point coplanar with L, M, N.
• Name a point coplanar with S, P, Q.

3
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
4
Rewrite each conditional statement in if-then form

• It is time for dinner if it is 6 pm.
• There are 12 eggs if the carton is full
• A number is divisible by 6 if it is divisible by
  2 and 3.
• An obtuse angle is an agle that measures more
  than 90 and less than 180.
• All students taking geometry have math during an
  even numbered block

5
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.

6
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
• If x2 36 then x 18 or x -18
• Thanksgiving is celebrated on a Thursday
• If youve visited Springfield, then youve been
  to Illinois.
• Two lines intersect in at most one point.

7
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 x is odd, then 3x is odd
• If m?P 90, then ?P is a right angle

8
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 x is odd, then 3x is odd
• If m?P 90, then ?P is a right angle

9
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 x is odd, then 3x is odd
• If m?P 90, then ?P is a right angle

10
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
11
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

12
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, then their intersection
   is a line. (16)

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

• The points E, F, and H lie in a plane
• The points E and F lie on a line

14
Use the diagram to state the postulate that
verifies the statement

• The planes Q and R intersect in a line
• The points E and F lie in plane R. Therefore,
  line m lies in plane R