1. 2.1 Conditional Statements

2. Goal 1: Recognizing Conditional Statement
A logical statement with 2 parts
2 parts are called the hypothesis & conclusion
Can be written in “if-then” form; such as, “If…, then…”
Hypothesis is the part after the word “If”
Conclusion is the part after the word “then”

3. Ex: Underline the hypothesis & circle the conclusion.
If you are a brunette, then you have brown hair.
hypothesis conclusion

4. Ex: Rewrite the statement in “if-then” form
Vertical angles are congruent.
If there are 2 vertical angles, then they are congruent.
If 2 angles are vertical, then they are congruent.

5. Ex: Rewrite the statement in “if-then” form
An object weighs one ton if it weighs 2000 lbs.
If an object weighs 2000 lbs, then it weighs one ton.

6. Counterexample Used to show a conditional statement is false.
It must keep the hypothesis true, but the conclusion false!

7. Ex: Find a counterexample to prove the statement is false.
If x2=81, then x must equal 9.
counterexample: x could be -9
because (-9)2=81, but x≠9.

8. Negation Writing the opposite of a statement. Ex: negate x=3 x≠3
Ex: negate t>5
t 5

9. Converse
Switch the hypothesis & conclusion parts of a conditional statement.
Ex: Write the converse of “If you are a brunette, then you have brown hair.”
If you have brown hair, then you are a brunette.

10. Inverse Negate the hypothesis & conclusion of a conditional statement.
Ex: Write the inverse of “If you are a brunette, then you have brown hair.”
If you are not a brunette, then you do not have brown hair.

11. Contrapositive
Negate, then switch the hypothesis & conclusion of a conditional statement (negate the converse)
Ex: Write the contrapositive of “If you are a brunette, then you have brown hair.”
If you do not have brown hair, then you are not a brunette.

12. Equivalent Statements
Equivalent Statements – both are true or both are false.
The original conditional statement & its contrapositive will always have the same meaning.
The converse & inverse of a conditional statement will always have the same meaning.

13. Goal 2: Using Point, Line, and Plane Postulates
Postulate 5: Through any 2 points, there exists exactly one line.
Postulate 6: A line contains at least 2 points.
Postulate 7: If two lines intersect, then their intersection is exactly one point.
Postulate 8: Through any 3 noncollinear points, there exists exactly one plane.
Postulate 9: A plane contains at least 3 noncollinear points.
Postulate 10: If 2 points lie in a plane, then the line containing them lies in the plane.
Postulate 11: If 2 planes intersect, then their intersection is a line.

14. Identifying Postulates
There is exactly one line (line n) that passes through the points A and B.
Line n contains at least two points, A and B.
Lines m and n intersect at point A.
Plane P passes through the noncollinear points A, B, and C.
Plane P contains at least three noncollinear points, A, B, and C.
Points A and B lie in plane P. So, line n, which contains points A and B, also lies in plane P.
Planes P and Q intersect. So, they intersect in a line, labeled in the diagram as line m.
Postulate 5
Postulate 6
Postulate 7
Postulate 8
Postulate 9
Postulate 10
Postulate 11