AMSCO'S Geometry. New York - Rye High School

Inverses, Converses, and Contrapositives 67EXAMPLE 3Write the inverse, converse, and contrapositive of the given conditional:If M is the midpoint of AB, then AM MB.Solution Inverse: If M is not the midpoint of AB, then AM MB.Converse: If AM MB, then M is the midpoint of AB.Contrapositive: If AM MB, then M is not the midpoint of AB.EXAMPLE 4Given the true statement, “If the polygon is a rectangle, then it has four sides,”which statement must also be true?(1) If the polygon has four sides, then it is a rectangle.(2) If the polygon is not a rectangle, then it does not have four sides.(3) If the polygon does not have four sides, then it is not a rectangle.(4) If the polygon has four sides, then it is not a rectangle.SolutionA conditional and its contrapositive always have the same truth value. Thecontrapositive of the given statement is “If a polygon does not have four sidesthen it is not a rectangle.”Answer (3)ExercisesWriting About Mathematics1. Samuel said that if you know that a conditional is true then you know that the converse ofthe conditional is true. Do you agree with Samuel? Explain why or why not.2. Kate said that if you know the truth value of a conditional and of its converse then youknow the truth value of the inverse and the contrapositive. Do you agree with Kate?Explain why or why not.Developing SkillsIn 3–6, for each statement, write in symbolic form:a. the inverse b. the converse c. the contrapositive.3. p → q 4. t → w 5. m → p 6. p → q