## Monday, July 16, 2007

### Geometry Chapter 2.1 Conditional Statements

Geometry chapter 2.1 Conditional Statements:

I) Vocabulary:

A. Conditional Statements - (if-then) - has two parts:

1. Hypothesis - (if)

2. Conclusion - (then)

Example: If it is noon in Georgia, then it is 9 am in California.

B) Converse Statement: Switch the hypothesis and conclusion of a Conditional Statement.

Example: If it is 9 am in California, then it is noon in Georgia.

C) Inverse Statement: negate both the hypothesis and conclusion of a Conditional Statement.

Example: If it is not noon in Georgia, then it is not 9 am in California.

1) Negation - write the negative of the statement.
Example: Statement: Angle A is acute.
Negation: Angle A is not acute.
or
It is not true that angle A is acute.
D) Contrapositive Statement: Switch and negate both the Hypothesis and Conclusion of a Conditional Statement.

Example: If it is not 9 am in California, then it is not noon in Georgia.

E) Equivalent Statements: 2 statements that are both true or both false, they have the same truth value. Contrapositive statements is always equivalent to its Conditional statement. The converse statement is always equivalent to its inverse statement.

F) Counterexample: An example that shows that a conditional statement is false.

Example: If x2 = 25, then x = 5
A counterexample is x = (-5) because (-5)2 = 25 but 5 is not equal to (-5)

II) Postulates:

#5) Postulate 5: Through any 2 points there exists one line.
#6) Postulate 6: A line contains at least two points.
#7) Postulate 7: If two lines intersect, then their intersection is exactly one point.
#8) Postulate 8: Through any three noncollinear points there exists exactly one plane.
#9) Postulate 9: A plane contains at least three noncollinear points.
#10) Postulate 10: If two points lie in a plane, then the line containing them lies in the plane.
#11) Postulate 11: If two planes intersect, then their intersection is a line.