1. Opener 5. If a number greater than 2 is even, then it’s not prime
Write the converse:
If M is the midpoint of AB, then AM = MB
If AB+BC=AC, then A, B, and C are collinear.
Write the inverse:
3. If |x| = 6, then x = 6 or –6
4. You score a goal if the ball crosses the line.
Write the contrapositive:
5. If a number greater than 2 is even, then it’s not prime

2. Sect. 2.2 Definitions and BiConditional Statements.
Goal Recognizing and Using Definitions
Goal Using Biconditional Statements

3. Recognizing and Using Definitions
PERPENDICULAR LINES are two lines that intersect to form a right angle. 
The symbol used for perpendicular lines is an upside down T, ()  .  In diagram, m  k.  

4. Recognizing and Using Definitions
A line perpendicular to a plane is a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.
n  B

5. Points A, B, and C are collinear.
Recognizing and Using Definitions
Decide if each statement about the diagram is true. Explain your answer with any postulates or definitions.
Points A, B, and C are collinear.
True, points are collinear if they lie on the same line.
b) is perpendicular to
False, DBC is not a right angle.
c) Points A, B, and D are noncoplanar.
False, three noncollinear points determine a plane.

6. We have pizza for lunch, only if it is Wednesday Hypothesis Conclusion
Using Biconditional Statements
Conditional Statements are not always written in If-Then form. Another common form of the conditional statement is the “only-if” form.
WARNING!!! The hypothesis does not follow the word if in the “only-if” statements.
Example:
We have pizza for lunch, only if it is Wednesday
Hypothesis Conclusion
Write in If, then form
If we have pizza for lunch, then it is Wednesday

7. Mrs. Kagan watches T.V., only if she has no book to read.
Using Biconditional Statements
Example:
Mrs. Kagan watches T.V., only if she has no book to read.
Hypothesis Conclusion
Write in If, then form
If Mrs. Kagan is watching T.V. then she has no book to read.

8. Using Biconditional Statements
Biconditional Statement: Statement that contains the phrase “if and only if”.
Writing a biconditional statement is the same as writing a conditional statement and its converse.
A biconditional statement can be true or False. To be true, both the statement and converse must be true.

9. Using Biconditional Statements
Rewriting a Biconditional statement
Rewrite the Biconditional statement as a Conditional Statement and its Converse.
Two lines intersect if and only if their intersection is exactly one point
Conditional: If two lines intersect, then they intersect in exactly one point.
Converse: If two lines contain exactly one point, then the two lines intersect.

10. x2 < 49 if and only if x < 7
Using Biconditional Statements
Given the following Conditional Statement:
If x2 < 49, then x < 7
Find each of the following:
a) The Converse
If x < 7, then x2 < 49
b) A Biconditional Statement
x2 < 49 if and only if x < 7 No
c) Is the Biconditional statement true? Why?

11. Two angles are complementary if and only if their sum is 90°
Using Biconditional Statements
Rewrite the biconditional statement as a conditional statement and its converse.
Two angles are complementary if and only if their sum is 90°
Conditional – If two angles are complementary, then their sum is 90°.
Converse – If the sum of two angles is 90°, then they are complementary.

12. Homework
– 38 even