C Challenge

Write a statement beginning with all, some, or no to match each Venn diagram.

43. 

44. 

45. 

46. Let a represent an integer. Consider the five statements r, s, t, u, and v.

    • r: a is even.
    • s: a is odd.
    • t: 2a is even.
    • u: 2a is odd.
    • v : 2 a + 1 v colon , 2 eh plus , 1  is odd.

    How many statements of the form p → q p rightwards arrow q  can you make from these statements? Decide which are true, and provide a counterexample if they are false.

Standardized Test Prep

SAT/ACT

47. Which conditional and its converse are both true?
    1. If x = 1 , x equals , 1 comma  then 2 x = 2 . 2 x equals , 2 .
    2. If x = 2 , x equals , 2 comma  then x 2 = 4 . x squared , equals 4 .
    3. If x = 3 , x equals , 3 comma  then x 2 = 6 . x squared , equals 6 .
    4. If x 2 = 4 , x squared , equals 4 comma  then x = 2 . x equals , 2 .
48. What is the midpoint of the segment with endpoints ( – 3 , 7 ) open en dash 3 comma 7 close  and (9, 5)?
    6. (6, 12)
    7. (2, 4)
    8. (3, 6)
    9. (6, 6)

49. Which is the best description of the figure below?

    

    1. convex pentagon
    2. concave octagon
    3. convex polygon
    4. concave pentagon

Short Response

50. Describe how to form the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13…

Mixed Review

See Lesson 2-1.

Find a counterexample to show that each statement is false.

51. You can connect any four points to form a rectangle.
52. The square of a number is always greater than the number.

See Lesson 1-8.

Find the perimeter of each rectangle with the given base and height.

53. 6 in., 12 in.
54. 3.5 cm, 7 cm
55. 1 3 4  yd  , 18  in  . 1 , and 3 fourths . yd , comma 18 , in , .
56. 11 m, 60 cm

Get Ready! To prepare for Lesson 2-3, do Exercises 57 and 58.

See Lesson 2-2.

Write the converse of each statement. Then determine the truth value of the original statement and of the converse.

57. If today is September 30, then tomorrow is October 1.
58. If A B ¯ eh b bar  is the perpendicular bisector of C D ¯ , c d bar , comma  then A B ¯ eh b bar  and C D ¯ c d bar  are perpendicular.

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