1. Section 2.1 Conditional Statements
Chapter 2
Section 2.1
Conditional Statements

2. Warm-Up Name a point collinear with N and U. X
Name a point coplanar with L, M, R S
Name a point coplanar with L, M, N. Q or T
Name a point coplanar with S, P, Q L

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.
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.

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. The equation 4x – 3 = 12 + 2x has exactly one solution
Decide whether the statement is true or false. If it is false, give a counter example
The equation 4x – 3 = x 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
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.

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 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

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 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

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 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

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
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

12. 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)

13. 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

14. 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