Section 2-4: Biconditionals and Good Definitions Rigor – Write Biconditional statements and differentiate between a good or bad definition. Relevance –

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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 180 o.

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 Biconditional: Two angles are congruent if and only if they have equal measures.

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.

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

Explain why the following are not good definitions. A fish is an animal that swims. Rectangles have 4 corners. Giraffes are animals with very long necks

Your Turn! 2-4 Classwork From the Core book Pg 68 #1 – 3 Pg 69 #1, 3, 4, 5, 7 Pg 70 #1, 2

Homework – project part 2 You now have the tools to complete task 2 of your project! Remember, the project is due no later than Friday, October 9 th. If you finish early, turn it in!