1. Subject Matter:
Bi-conditionals and Definitions
Objective
Pacing
To write bi-conditionals and recognize good definitions.
1 day
Standards
G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contra-positive of a conditional statement.
G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

2. Problem 1: Writing a Biconditional
What is the converse of the following conditional? If the converse is also true, rewrite the statements as a biconditional.
A. If the sum of the measures of two angles is 180, then two angles are supplementary.

3. B. If two angles have equal measures, then the angles are congruent.

4. Problem 2: Identifying the Conditional in a Biconditional
What are the two biconditional statements that form this bicondtional?
A. A ray is an angle bisector if an only if it divides an angle into two congruent angles.

5. B. Two numbers are reciprocals if and only if their product is 1.

6. Problem 3: Writing a Definition as a Biconditional
Is this definition of quadrilateral reversible? If yes, write it as a true biconditional.
A. A quadrilateral is a polygon with four sides.

7. B. A straight angle is an angle that measures 180.

8. Problem 4: Identifying Good Definitions
A. Multiple Choice Which of the following is a good definition.
A fish is an animal that swims.
Rectangles have four corners.
Giraffes are animal with very long necks.
A penny is a coin worth one cent.

9. Components of a Good Definition:
A good definition is reversible.
A good definition uses clearly defined terms.
A good definition is precise.
Components of a Good Definition:

10. Is the following statement a good definition? Explain.
A square is a figure with four right angles.

11. Close the instruction by asking: Q: What is the definition of a biconditional? [A statement is a biconditional if and only if both the statement and its converse are true.]
Assignment Guide:
Practice: Do # 7-29, odd pages
Classwork: Do Practice Biconditionals and Definitions Form G
Homework: Do # 8-30, even pages