1. 2.4 Conditional Statements
Geometry
2.4 Conditional Statements

2. Goal 1: Using Conditional Statements
Logic = Reasoning
Logical statements can be written
as a conditional statement also known as
an If (hypothesis) , then (conclusion).
If an angle has a measure of 90o,
then the angle is a right angle.

3. Parts of a conditional statement
A conditional statement can be broken up into two parts. The statement after the If is called the hypothesis and the statement after the then is called the Conclusion.
If an angle has a measure of 90o,
then the angle is a right angle.
What is the hypothesis?
What is the conclusion?

4. The Converse
If p, then q. were p is the hypothesis and q is the conclusion.
The converse is formed by switching the hypothesis and the conclusion.

5. The Converse (cont’d) If an angle has a measure of 90o,
then the angle is a right angle.
If the angle is a right angle,
then the angle has a measure of 90o.
Example: If I practice well, then I will play
Hypothesis:
Conclusion:
Converse:

6. Truths and Counterexamples
Given conditional statements are always assumed to be true.
A converse is true only if a counterexample (one example that contradicts the conditional statement) can not be found to disprove the converse statement.
If the car is running, then the keys are in the ignition.
Is the converse true?

7. Biconditional Statement
A biconditional statement or “p if and only if q” is written when a conditional statement AND its converse is always true.
If A is a right angle, then its measure is 90o.
If A has a measure of 90o, then it is a right angle.
A is a right angle if and only if its measure is 90o.

8. Goal 2: Point, Line, and Plane Postulates
Through any two distinct points there exists exactly one line.
A line contains at least two points.
Through any three noncollinear points there exists exactly one plane.
A plane contains at least three noncollinear points
If two distinct points lie in a plane, then the line containing them lies in the plane.
If two distinct planes intersect then their intersection is a line.