Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-2 Conditional Statements - Lesson Check: 2

Answer

conditional true converse false inverse false contrapositive true

Work Step by Step

Since a rectangle with these measurements does have a perimeter of 10, the conditional is true. The converse swaps the hypothesis and conclusion. If a figure has a perimeter of 10 cm then it is a rectangle with sides of 2 cm and 3cm. The converse is false because a 1 cm x 4 cm rectangle also has a perimeter of 10. The inverse negates the hypothesis and conclusion. If a figure is not a rectangle with sides of 2 cm and 3 cm, then it does not have a perimeter of 10 cm. The inverse is false because a 1 cm x 4 cm rectangle also has a perimeter of 10. The contrapositive both negates and swaps the hypothesis and conclusion. If a figure does not have a perimeter of 10 cm then the figure is not a rectangle with sides of 2 cm and 3 cm. The contrapositive is true because a 2 cm x 3 cm rectangle does have a perimeter of 10 cm.
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