C Challenge

Draw D G ¯ . d g bar , .  Construct a quadrilateral with diagonals that are congruent to D G ¯ , d g bar , comma  bisect each other, and meet the given conditions. Describe the figure.

30. The diagonals are not perpendicular.
31. The diagonals are perpendicular.

Construct a rectangle with side lengths a and b that meets the given condition.

32. b = 2 a b equals 2 eh
33. b = 1 2 a b equals . 1 half , eh
34. b = 1 3 a b equals . 1 third , eh
35. b = 2 3 a b equals . 2 thirds , eh

Construct a triangle with side lengths a, b, and c that meets the given conditions. If such a triangle is not possible, explain.

36. a = b = c eh equals . b equals c
37. a = b = 2 c eh equals . b equals 2 c
38. a = 2 b = 2 c eh equals . 2 b equals 2 c
39. a = b + c eh equals . b plus c

Standardized Test Prep

SAT/ACT

40. The diagram below shows the construction of C P ↔ modified c p with left right arrow above  perpendicular to line l through point P. Which of the following must be true?

    1. C B ↔ || A B ↔ modified c b with left right arrow above , vertical linevertical line , modified eh b with left right arrow above
    2. C P = 1 2 A B c p equals . 1 half eh b
    3. A C ↔ || C B ↔ modified eh c with left right arrow above , vertical linevertical line , modified c b with left right arrow above
    4. A C ¯ ≅ B C ¯ eh c bar , approximately equal to , b c bar

    

41. Suppose you construct lines l, m, and n so that l ⊥ m l up tack m  and l || n . l vertical linevertical line n .  Which of the following is true?
    6. m || n m vertical linevertical line n
    7. m || l m vertical linevertical line l
    8. n ⊥ l n up tack l
    9. n ⊥ m n up tack m

    Short Response

42. For any two points, you can draw one segment. For any three noncollinear points, you can draw three segments. For any four noncollinear points, you can draw six segments. How many segments can you draw for eight noncollinear points? Explain your reasoning.

    

Mixed Review

See Lesson 3-5.

Find each missing angle measure.

Get Ready! To prepare for Lesson 3-7, do Exercises 45–47.

See p. 831.

Simplify each ratio.

45. 2 − ( − 3 ) 6 − ( − 4 ) fraction 2 minus . open , negative 3 , close , over 6 minus . open , negative 4 , close end fraction
46. 1 − 4 − 2 − 1 fraction 1 minus 4 , over negative 2 minus 1 end fraction
47. 12 − 6 2 − 5 fraction 12 minus 6 , over 2 minus 5 end fraction

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