Geometry Section 2.1 on Conditional Statements and the point line and plane postulates.

1. Unit 2. Section 2.1
CONDITIONAL STATEMENTS

2. - Conditional statements are used in every field
of human endeavor.
- They are crucial to the search for truth
- If you are going to be able to adequately
interpret and judge the statements you hear,
you must understand the structure of
Conditional statements.
-
WARNING: Once you get good at these, you
may be amused by statements made by
politicians and other public speakers.

3. Objectives
 Students will be able to:
 Identify conditional statements and place them in
if-then form
 Identify the hypothesis and conclusion of a
conditional statement
 Convert conditional statements into their other
logical variants
 Identify and use truth relationships of conditional
statements
 State and use the point, line and plane postulates
of geometry

4. What is a Conditional
Statement?
 A statement that can be written in the
format:
If …., then ….
 The part after “if” is called the hypothesis
 Do not confuse this with the word “hypothesis”
from science
 The rest (after “then”) is the conclusion

5. Statements Not in If-Then Form
- Often statements are not in if –then form, but to
test them out scientifically, we must convert them
- In English, there are infinite ways to rephrase a
conditional statement; however, we will cover the
three most common variations here

6. Standard Sentence
 Split the subject and predicate.
 Add “If it is” or “If they are” to the subject
 Add “then it” or “then they” to the predicate
 Smooth out the grammar
 Example: “All dogs go to heaven.”
 “If they are dogs, then they go to heaven.”

7. “Whenever” or “When”
 Replace “whenever” or “when” with “if”
 Add “then” after the comma
 Example: “Whenever I see a seagull, I think of
home.”
 If I see a seagull, then I think of home.

8. “If” at the end
 Move the “if” clause to the beginning
 Add “then” after the “if” clause
 Example: “I eat if I am hungry.”
 “If I am hungry, then I eat.”

9. Logical Variations of the
Conditional
-Often a conditional statement can be difficult to
prove or unwieldy to use.
- By using logical variations, we find forms easier to
prove or use.

10. Converse, Inverse, &
Contrapositive
 Converse: formed by swapping the
hypothesis and the conclusion
 Inverse: formed by negating the hypothesis
and conclusion
 Contrapositive: formed by both negating and
swapping the hypothesis and conclusion

11. Equivalent Statements
 If the Conditional is true (or false) then so is
the Contrapositive and vice versa.
 Similarly, if the Converse is true, then so is the
Inverse and vice versa
 If both the Conditional and its Converse are
true, then they can be rewritten as a
Biconditional statement (more next class)

12. Example 1
 If you added 2+2, you got 4
 CONVERSE:
If you got 4, then you added 2+2.
 INVERSE:
If you did not add 2+2, you did not get 4.
 CONTRAPOSITIVE:
If you did not get 4, then you did not add 2+2.

13. Example 2 (the word “not”)
 If you do not eat, you will be hungry
 CONVERSE:
If you are hungry, then you did not eat.
 INVERSE:
If you ate, then you are not hungry.
 CONTRAPOSITIVE:
If you are not hungry, then you ate.

14. Point, Line and Plane Postulates

15. Point, Line & Plane Postulates
5. Through any two points there exists exactly one line.
6. A line contains at least two points.
7. If two lines intersect, then their intersection is exactly
one point.
8. Through any three noncollinear points there exists
exactly one plane.
9. A plane contains at least three noncollinear points.
10. If two points lie in a plane, then the line containing
them lies in the plane.
11. If two planes intersect, then their intersection is a
line.

16. Reference
 McDougal Littell Geometry (2001), Section
2.1