Section 2-4: Biconditionals and Good Definitions

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Presentation transcript:

Section 2-4: Biconditionals and Good Definitions Rigor – Write Biconditional statements and differentiate between a good or bad definition. Relevance – Develop logical reasoning skills; including precision, clarity, and truth; needed to defend ideas and theories.

Notes: Biconditional Statements A biconditional statement is a single true statement that combines a true conditional with its true converse. Notation: or p iff q (“if and only if”) Example: Two angles are supplementary if and only if the sum of their measures is 180o.

Ex: Write the converse, list the truth values, & write biconditional if possible. Conditional: “If 2 angles have equal measures, then the angles are congruent.” Converse: If 2 angles are congruent, then they have equal measures. True True Biconditional: Two angles are congruent if and only if they have equal measures.

Converse: If 2 angles are congruent, then they are vertical angles. Ex: Write the converse, list the truth values, & write biconditional if possible. Conditional: “If 2 angles are vertical, then the angles are congruent.” Converse: If 2 angles are congruent, then they are vertical angles. True False Biconditional is not possible because converse is false.

Good definitions…are they really necessary? Draw a polygon with 4 right angles. We will compare our drawings with the class.

Good definitions must: Use clearly understood terms (common terms or already defined) Are precise. Avoid generic words such as large and almost. Are reversible. Any good definition can be written as a biconditional.

A straight angle is an angle that measures 180o. Ex: Is this a good definition? If so, write the definition as a biconditional. A straight angle is an angle that measures 180o.

Explain why the following are not good definitions. A fish is an animal that swims. Giraffes are animals with very long necks

2-4 Classwork from the Workbook Pg 68 #1 – 3 Pg 69 Odds Pg 70 #1, 2 Be ready to discuss answers in 20 min

2-4 Honors Assignments Primary Assignment: Quizizz Submit answers online: join.quizizz.com by 7AM Codes: Period 1: 528506 Due Thursday Period 5: 115163 Due Thursday Period 6: 892403 Due Friday Secondary Assignment: Textbook page 99 #10 – 19

2-4 Standard Assignments Primary Assignment: Quizizz Submit answers online by Friday at 7AM Codes: Period 2: Period 4: Period 7: Secondary Assignment: Textbook page 99 #10 – 19