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This lesson explores the concepts of conditional statements, converses, and biconditionals in geometry. We will analyze the truth values of a conditional and its converse through a specific example related to angle sums. Additionally, we will complete a sequence of perfect squares and engage in a fun activity where you create a clear and precise definition for an object or term. This exercise emphasizes the importance of clarity and reversibility in definitions, providing a solid foundation for understanding logical statements in mathematics.
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Bellwork Babies are cute. a) Write its conditional statement. b) Write its converse. c) Write the truth value of a and b. 2) Is the converse of the following conditional true? If the sum of two angles equals 180, then they are supplemental. 3) Finish the sequence 1, 4, 9, 25, 36, … 4) Trivia
Biconditionals When both the conditional and its converse are true, the statement is called a biconditional. You can write a biconditional as a statement using if and only if:
Example If three points are collinear, then they lie on the same line. true If three points lie on the same line, then they are collinear. True Biconditional Three points are collinear if and only if they lie on the same line.
Super Fun Activity Pick an object in the room or a word and write a definition of it. Be creative. Don’t be lame.
Good Definitions • Clear terms, that are already defined • Precise (don’t use vague words like large, sort of, almost) • It’s reversible (you can write it as a biconditional)
Examples: • A triangle has sharp corners. -imprecise word: sharp -no reversible • A square is a figure with four right angles. • Counter example
