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KEY CONCEPT: BICONDITIONAL STATEMENTS EXAMPLE 1: WRITING A BICONDITIONAL What is the converse of the following true conditional? If the converse is also true rewrite the statement as a biconditional. If the sum of the measures of two angles is 180, then the two angles are supplementary. Converse: If two angles are supplementary, then the sum of the two angles is 180. Biconditional: Two angles are supplementary if and only if the sum of the measures of the two angles is 180. EXAMPLE 2: IDENTIFYING THE CONDITIONALS IN A BICONDITIONAL What are the two conditional statements that form this biconditional? A ray is an angle bisector if and only if it divides an angle into two congruent angles. 𝒑: A ray is an angle bisector. 𝒒: A ray divides an angle into two congruent angles. 𝒑 → 𝒒: If a ray is an angle bisector, then it divides an angle into two congruent angles. 𝒒 → 𝒑: If a ray divides an angle into two congruent angles, then it is an angle bisector. EXAMPLE 3: WRITING A DEFINITION AS A BICONDITIONAL Is this definition of quadrilateral reversible? If yes write it as a true biconditional. A quadrilateral is a polygon with four sides. Conditional Statement: If a figure is a quadrilateral, then it is a polygon with four sides. Converse: If a figure is a polygon with four sides, then it is a quadrilateral. Biconditional: A figure is a quadrilateral if and only if it is a polygon with 4 sides. EXAMPLE 4: IDENTIFYING GOOD DEFINITIONS Which of the following is a good definition? A. A fish is an animal that swims. B. Rectangles have four corners. C. Giraffes are animals with very long necks. D. A penny is a coin worth one cent. ASSIGNMENT: Pg 101 – 102 #’s 8 – 38 even.