1. By writing biconditional statements, students will clarify definitions inside or outside of mathematics, then they will use these definitions in discussion with others and in their own reasoning.

2. 2-3 Biconditionals and Definitions
To write biconditionals
To recognize good definitions

3. Definition
When a conditional and its converse are true, you can combine them as a true biconditional. This is the statement you get by connecting the conditional and its converse with the word and. You can write a biconditional more concisely, however, by joining the two parts of each conditional with the phrase if and only if.

7. What is a good definition?

11. 2-3 Quiz
The following questions are designed to help you determine whether or not you truly understood the lesson. Please get with me if you don’t understand why you missed the ones you did. Record the number you get right on your portfolio sheet!

12. 1. Determine whether the conditional and its converse are both true
1. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If two lines are parallel, they do not intersect. If two lines do not intersect, they are parallel.
One statement is false. If two lines do not intersect, they could be skew..
One statement is false. If two lines are parallel, they may intersect twice.
Both statements are true. Two lines are parallel if and only if they do not intersect.
Both statements are true. Two lines are not parallel if and only if they do not intersect.

13. 2. Write the two conditional statements that make up the following biconditional. I drink juice if and only if it is breakfast time.
I drink juice if and only if it is breakfast time. It is breakfast time if and only if I drink juice.
If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice.
If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time.
I drink juice. It is breakfast time.

14. The statement is not reversible.
3. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional. Two lines that intersect at right angles are perpendicular.
The statement is not reversible.
Reversible; if two lines intersect at right angles, then they are perpendicular.
Reversible; if two lines are perpendicular, then they intersect at right angles.
Reversible; two lines intersect at right angles if and only if they are perpendicular.

15. 4. Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides.
A six-sided figure can have four sides congruent.
Some triangles have all sides congruent.
A square has four congruent angles.
A rectangle has four sides.

16. 5. Which biconditional is NOT a good definition?
A whole number is odd if and only if the number is not divisible by 2.
An angle is straight if and only if its measure is 180.
A ray is a bisector of an angle if and only if it splits the angle into two angles.
A whole number is even if and only if it is divisible by 2.

17. ASSIGNMENT
2-3 p #8-46 even