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Understanding Definitions and Biconditional Statements in Geometry

This lesson focuses on the concept of definitions in geometry, particularly how to create and analyze biconditional statements. Students will learn what constitutes a valid definition, specifically for terms like "flopper." Through group activities, they will write definitions, trade them, and explore conditional and converse statements. Important concepts such as "if and only if" will be discussed, showcasing how both must hold true for biconditional statements. Examples will clarify how accurate definitions support logical reasoning in mathematics, ensuring a solid foundation in geometric principles.

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Understanding Definitions and Biconditional Statements in Geometry

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  1. 2.3 Definitions Obj: To understand what it means to be a definition and write biconditional statements

  2. Flopper or Not a Flopper Definitions need to be specific and concise Look at page 99 in your textbook. Look at cards 1 and 2: With your group write a definition for a flopper

  3. Trade definitions with another group • Look at card 3, which letters would be considered floppers by their definition?

  4. Return to original group. • Group: Did they pick the letters you thought they would?

  5. For definitions the conditional statement and converse are always both true. Biconditional: When the hypothesis and conclusion are joined by the statement “if and only if”. If and only if = _________ *Use when both the ________________ and ____________________ are true.

  6. Example • Conditional: If 2 angles are supplementary, then the sum of their measures is 180. • Converse: _________________________ ___________________________________ • Both the conditional and converse are true so write the biconditional • Biconditional _______________________ ___________________________________

  7. Definitions and Biconditionals • If a statement is a definition then the biconditional MUST be true Ex: Acute angles are angles with a measure between 0° and 90°. Conditional: If it is an acute angle, then the measure is between 0° and 90°. Converse: If the measure of an angle is between 0° and 90°, then the angle is acute. * Both the conditional and converse are true therefore it is a definition

  8. Activity 2 Adjacent angles angles in a plane that have their vertex and one side in common, but have no common interior points.

  9. Below are Definitions Write the definition as a conditional, then write the converse of each conditional A square is a quadrilateral with 4 congruent sides and 4 congruent angles. If it is a square, then it has 4 congruent sides and 4 congruent angles. If it has 4 congruent sides and 4 congruent angles then it is a triangle. A right angle is an angle whose measure is 90 degrees. If it is a right angle, then its measure is 90 degrees. If an angle’s measure is 90 degrees, then it is a right angle.

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