Section 2 4 Biconditionals and Good Definitions Rigor

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 n. A biconditional statement is a single true statement that combines a true conditional with its true converse. n Notation: (“if and only if”) n Example: or p iff q 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 True 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. ” True Converse: If 2 angles are congruent, then they are vertical angles. 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: n Use precise words. Avoid generic words such as large and almost. n Be able to be written as a biconditional statement. (conditional and converse are both true)

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

Ex: Is this a good definition? If so, write the definition as a biconditional. Giraffes are animals with very long necks.

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

2 -4 Standard Assignments n. Primary Assignment: join. quizizz. com ¨Submit answers online by at 7 AM ¨Codes: § Period 1: § Period 3: Due Thursday § Period 7: Due Friday Due Thursday n. Secondary Assignment: ¨ Textbook page 99 #10 – 19

2 -4 Honors Assignments n. Primary Assignment: join. quizizz. com ¨Submit answers online by 7 AM on Friday ¨Codes: § Period 2: § Period 4: § Period 6: n. Secondary Assignment: ¨ Textbook page 99 #10 – 19