Practice and Problem-Solving Exercises

See Problem 1.

A Practice Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.

7. If two segments have the same length, then they are congruent.
8. Algebra If x = 12 , x equals , 12 comma  then 2 x – 5 = 19 . 2 x en dash , 5 equals , 19 .
9. If a number is divisible by 20, then it is even.
10. Algebra If x = 3 , x equals , 3 comma  then | x | = 3 . vertical line x vertical line equals 3 .
11. In the United States, if it is July 4, then it is Independence Day.
12. If p → q p rightwards arrow q  is true, then ˜ q → ˜ p tilde q rightwards arrow tilde p  is true.

See Problem 2.

Write the two statements that form each biconditional.

13. A line bisects a segment if and only if the line intersects the segment only at its midpoint.
14. An integer is divisible by 100 if and only if its last two digits are zeros.
15. You live in Washington, D. C., if and only if you live in the capital of the United States.
16. A polygon is a triangle if and only if it has exactly three sides.
17. An angle is a right angle if and only if it measures 90.
18. Algebra x 2 = 144 x squared , equals 144  if and only if x = 12 x equals , 12  or x = − 12 . x equals negative 12 . .

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