How do you determine whether a definition is reversible?
Write the definition as a conditional and the converse of the conditional. If both are true, the definition is reversible.
Is this definition of quadrilateral reversible? If yes, write it as a true biconditional.
Definition: A quadrilateral is a polygon with four sides.
Think | Write |
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Write a conditional. | Conditional: If a figure is a quadrilateral, then it is a polygon with four sides. |
Write the converse. | Converse: If a figure is a polygon with four sides, then it is a quadrilateral. |
The conditional and its converse are both true. The definition is reversible. Write the conditional and its converse as a true biconditional. | Biconditional: A figure is a quadrilateral if and only if it is a polygon with four sides. |
Is this definition of straight angle reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180.
One way to show that a statement is not a good definition is to find a counterexample.
Multiple Choice Which of the following is a good definition?
How can you eliminate answer choices?
You can eliminate an answer choice if the definition fails to meet any one of the components of a good definition.
Choice A is not reversible. A whale is a counterexample. A whale is an animal that swims, but it is a mammal, not a fish. In Choice B, corners is not clearly defined. All quadrilaterals have four corners. In Choice C, very long is not precise. Also, Choice C is not reversible because ostriches also have long necks. Choice D is a good definition. It is reversible, and all of the terms in the definition are clearly defined and precise. The answer is D.
Is the following statement a good definition? Explain.
A square is a figure with four right angles.