1. Bell Work
1) Write the statement in “If/Then” Form. Then write the inverse, converse, and contrapositive:
a) A linear pair of angles is supplementary.
b) The measure of a right angle is 90°.
2) Find the measure of Angle ABD. What classification does it have? A B E C D 35 75 70

2. Outcomes I will be able to: 1) Define perpendicular lines
2) Recognize and use biconditional statements.

3. Agenda 1) Bell Work 2) Outcomes 3) Perpendicular definitions
4) Biconditional definition

4. 2.2 Definitions and Biconditional Statements
In Lesson 1.2 we learned that a definition uses known words to describe a new word. Here are two examples.

5. Perpendicular Lines What does it mean to be perpendicular?
Perpendicular Lines – Two lines are called perpendicular lines if they intersect to form a right angle(90°).
Symbolically -
Signifies right angle

6. Perpendicular Lines Can a line be perpendicular to a plane?
Perpendicular to a plane: A perpendicular to a plane is a line that intersects the plane in a point and is perpendicular to every line the plane that it intersects. The symbol is read “perpendicular to.”

7. Using Definitions
Using the diagram and definitions from Chapter 1, decide if the following statements are true
True – all points lie on same line
True – The lines form a right angle
False – The angles do not share a side

8. Conditional Statements
Are all conditional statements always written in “if-then” form?
Some conditional statements are written in “only-if” form
Example:
It is Saturday, only if I am working at the store
Hypothesis Conclusion
Rewrite in “If/then” form
If it is Saturday, then I’m working at the store

9. Biconditional Statements
Biconditional Statement - a statement that contains the phrase “if and only if.”
It is equivalent to writing a conditional statement, and its converse
Example: Three points are coplanar if and only if they lie on the same plane
Conditional – If three points are coplanar, then they lie on the same plane
Converse - If three points lie on the same plane, then they are coplanar

10. Example 2 If three lines are coplanar, then they lie in the
same plane.
If three lines lie in the same plane, then they are coplanar.
Are both the conditional statement and the converse true?
Yes
Is this biconditional true?
Yes

11. Biconditional Statements
Are all biconditional statements true?
***To be true, both the conditional and the converse of a biconditional statement must be true
Ex 3: Consider the following statement:
x = 3 if and only if x² = 9
a) Is this a biconditional statement?
Yes, it contains if and only if
b) Is it true?
Conditional – If x = 3, then x² = 9.
Converse – If x² = 9, then x = 3.

12. White Board Practice
Conditional Statement - If two points lie in a plane, then the line containing them lies in the plane.
Write this as a biconditional statement
Biconditional – Two points lie in a plane, if and only if the line containing them lies in the plane
Is this true or false?

13. Example 4
Each of the following statements is true. Write the converse of each statement and decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample.
A) If two points lie in a plane, then the line containing them lies in the plane.
B) If a number ends in 0, then the number is divisible by 5.

14. Using Biconditionals to help with Proofs
Knowing how to use true biconditional statements is an important tool for reasoning in geometry. For instance, if you can write a true biconditional statement, then you can use the conditional statement or the converse to justify an argument.

15. Example 5
The converse of the Angle Addition Postulate is true. Write the converse and combine it with the postulate to form a true biconditional statement.
Angle Addition Postulate: If P is in the interior of ∠RST, then the m∠RSP + m∠PST = m∠RST.
Converse: If m∠RSP + m∠PST = m∠RST , then P is in the Interior of ∠RST.
Biconditional: P is in the interior of ∠RST if and only if m∠RSP + m∠PST = m∠RST .

16. Exit Quiz
Given the following conditional statement, write as converse, inverse, contrapositive, and biconditional statements
Determine if each is true or false, and explain why.
Conditional – If I am at Herron, I am at school
Converse –
Inverse –
Contrapositive –
Biconditional -