2-3: Biconditionals and Definitions

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Presentation transcript:

2-3: Biconditionals and Definitions

Biconditionals A biconditional is a single true statement that combines a true conditional and its true converse. You can write a biconditional by joining the two parts with the phrase if and only if. A definition is considered “good” if it can be written as a biconditional statement. A point is a midpoint if and only if it divides a segment into two congruent segments. (p ↔ q)

Writing a Biconditional What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional. If the sum of the measures of two angles is 180, then the two angles are supplementary. If two angles have equal measure, then the angles are congruent.

Identifying the Conditionals in a Biconditionals 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. Two numbers are reciprocals if and only if their product is 1.

Definitions A good definition should: Use clearly understood terms Be precise Be reversible Is the definition of straight angle reversible? If so, write it as a true biconditional. A straight angle is an angle that measures 180.

Identifying Good Definitions One way to show that a statement is not a good definitions is to find a counterexample. Which of the following is a good definition? A fish is an animal that swims. Rectangles have four corners. Giraffes are animals with very long necks. A penny is a coin worth one cent.