1. 2.3 Biconditionals, and Definitions

2. Write biconditionals and recognize good definitions.
Objective:
Write biconditionals and recognize good definitions.
2.3 Biconditionals and Definitions

3. Biconditional If and only if Conditionals
Vocabulary:
Biconditional
If and only if
Conditionals
2.3 Biconditionals and Definitions

4. Solve it!
2.3 Biconditionals and Definitions

5. Biconditional
A single true statement that combines a true conditional and its true converse, you can write a biconditional by joining the two parts of each conditional with the phrase if and only if
Symbol:
2.3 Biconditionals and Definitions

6. Biconditional
2.3 Biconditionals and Definitions

7. Writing a Biconditional:
To write a biconditional first determine if the what is the converse of the following true conditional. If the converse is true then write a biconditional statement
Conditional: If the sum of the measure of two angles is 180, then the two angles are supplementary
Converse: If two angles are supplementary, then the sum of the measures of the two angles is 180
Biconditional:
Two angles are supplementary if and only if the sum of the measures of the two angles is 180
2.3 Biconditionals and Definitions

8. You Try
What is the converse of the following conditional, if the converse is true write a biconditional statement
If two angles have equal measures, then the angles are congruent
2.3 Biconditionals and Definitions

9. You Try Solution: Biconditional
If two angles have equal measures, then the angles are congruent
Converse: If angles are congruent, then they have equal measures
Biconditional
Two angles have equal measures if and only if they are congruent
2.3 Biconditionals and Definitions

10. Identifying the Parts:
2.3 Biconditionals and Definitions

11. Identifying the conditionals in a Biconditional:
What are the two statements that form a biconditional
A ray is an angle bisector if and only if it divides and angle into two congruent angles
Find p and q
2.3 Biconditionals and Definitions

12. Identifying the conditionals in a Biconditional:
A ray is an angle bisector if and only if it divides and angle into two congruent angles
P – A ray is an angle bisector
Q – A ray divides an angle into two congruent angles
Conditional: If a ray is an angle bisector, then it divides the angle into two congruent angles
Converse: If a ray divides and angle into two congruent angles, then it is an angle bisector
2.3 Biconditionals and Definitions

13. You Try!
What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is one.
2.3 Biconditionals and Definitions

14. You Try Solution: Conditional: If two numbers are reciprocals,
Two numbers are reciprocals if and only if their product is one.
Conditional: If two numbers are reciprocals,
then their product is one
Converse: If two numbers product is one,
then they are reciprocals.
2.3 Biconditionals and Definitions

15. Writing a Definition as a Biconditional:
Is this definition of quadrilateral reversible?
If yer, write it as a true biconditional.
Definition: A quadrilateral is a polygong with four sides.

16. Writing a Definition as a Biconditional:

17. Lesson Check:

18. Lesson Check: