See Problem 3.

Test each statement below to see if it is reversible. If so, write it as a true biconditional. If not, write not reversible.

19. A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to a segment at its midpoint.
20. Complementary angles are two angles with measures that have a sum of 90.
21. A Tarheel is a person who was born in North Carolina.
22. A rectangle is a four-sided figure with at least one right angle.
23. Two angles that form a linear pair are adjacent.

See Problem 4.

Is each statement below a good definition? If not, explain.

24. A cat is an animal with whiskers.
25. The red wolf is an endangered animal.
26. A segment is part of a line.
27. A compass is a geometric tool.
28. Opposite rays are two rays that share the same endpoint.
29. Perpendicular lines are two lines that intersect to form right angles.

B Apply

30. Think About a Plan Is the following a good definition? Explain.

    A ligament is a band of tough tissue connecting bones or holding organs in place.

    • Can you write the statement as two true conditionals?
    • Are the two true conditionals converses of each other?

31. Reasoning Is the following a good definition? Explain.

    An obtuse angle is an angle with measure greater than 90.

32. Open-Ended Choose a definition from a dictionary or from a glossary. Explain what makes the statement a good definition.
33. Error Analysis Your friend defines a right angle as an angle that is greater than an acute angle. Use a biconditional to show that this is not a good definition.
34. Which conditional and its converse form a true biconditional?
    1. If x > 0 , x greater than , 0 comma  then | x | > 0 . vertical line x vertical line greater than 0 .
    2. If x = 3 , x equals , 3 comma  then x 2 = 9 . x squared , equals 9 .
    3. If x 3 = 5 , x cubed , equals 5 comma  then x = 125 . x equals , 125 .
    4. If x = 19 , x equals , 19 comma  then 22 − 3 = 35 . 22 minus , 3 equals , 35 .

Write each statement as a biconditional.

35. Points in Quadrant III have two negative coordinates.
36. When the sum of the digits of an integer is divisible by 9, the integer is divisible by 9 and vice versa.
37. The whole numbers are the nonnegative integers.
38. A hexagon is a six-sided polygon.

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