Vocabulary

1. 2-2 Biconditionals & DefinitionsM11.B.2Objectives:1) To write biconditionals2) To recognize good definitions

2. Vocabulary • When a conditional and its converse are true, you can combine them as a true biconditional. **You write a biconditional by joining the two parts of each conditional with the phrase if and only if.

3. Example: Consider this true Conditional Statement • Write its converse. If the converse is also true, combine the statements as a biconditional. Conditional: If x = 5, then x + 15 = 20 Converse: Biconditional:

4. Example • Consider this true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. • Conditional: If three points are collinear, then they lie on the same line. • Converse: • Biconditional:

5. Example: Separating a Biconditional Into Parts • Write the two statements that form this biconditional. Lines are skew if and only if they are noncoplanar.

6. Using Symbols • COPY THE ORANGE BOX ON PAGE 76 INTO YOUR NOTEBOOKS!

7. Good Definitions **A good definition is a statement that can help you identify or classify an object. • Use clearly understood terms. The terms should be commonly understood or already defined. • Are precise. Avoid words such as: large, sort of, and some. • Are reversible. You can write it as a true biconditional. One way to show that a statement is NOT a good definition is to find a counterexample.

8. Example • Definition: A right angle is an angle whose measure is 90. • Conditional: • Converse: • Biconditional

9. Example • Is the following statement a good definition? Explain. ** A square is a figure with four right angles. ** A triangle has sharp corners.