2 3 Biconditionals and Definitions 2 3 Biconditionals

2. 3 Biconditionals, and Definitions 2. 3 Biconditionals and Definitions

Objective: • Write biconditionals and recognize good definitions. 2. 3 Biconditionals and Definitions

Vocabulary: • Biconditional • If and only if • Conditionals 2. 3 Biconditionals and Definitions

Solve it! 2. 3 Biconditionals and Definitions

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

Biconditional 2. 3 Biconditionals and Definitions

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

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

You Try Solution: • 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

Identifying the Parts: 2. 3 Biconditionals and Definitions

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

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

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

You Try Solution: 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

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.

Writing a Definition as a Biconditional:

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