Page 336 - Algebra 1

6. What is the relationship of the truth values of an original statement and its contrapositive?
7. To compare the truth values of the converse and inverse, complete the table for each original statement.
Original statement: If a figure is a square, then it is a rectangle.
Original statement: If an object has wheels, then it is a bicycle.
8. What is the relationship of the truth values of the converse and inverse of an original statement?
Investigation Practice
Write the given statement in the form indicated.
Original statement: If it is raining, then it is cloudy.
a. Write the contrapositive.
b. Write the converse.
c. Write the inverse.
d. Generalize If the original statement is true, what is the truth value of the
contrapositive?
e. Predict If the converse of a statement is false, what is the truth value of
the inverse of the statement?
Identify Statement 2 as the converse, inverse, or contrapositive of Statement 1. Then indicate the truth value of each statement.
f. Statement 1: If a figure is a rectangle, then it is not a triangle. Statement 2: If a figure is a triangle, then it is not a rectangle.
g. Statement 1: If a figure is not a polygon, then it is not a right triangle. Statement 2: If a figure is a polygon, then it is a right triangle.
True or False
Converse
Inverse
True or False
Converse
Inverse
Investigation 5 321