Chapter 2 - Reasoning and Proof - 2-2 Conditional Statements - Lesson Check - Page 92: 2

conditional true converse false inverse false contrapositive true

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.