C Challenge

33. Study the figures. Complete the definition of a line perpendicular to a plane: A line is perpendicular to a plane if it is ? ¯ modified question mark with under bar below to every line in the plane that ? ¯ . modified question mark with under bar below , .

    

    Line r ⊥ up tack  plane M.

    

    Line t is not ⊥ up tack  plane P.

34. 1. Use your compass to draw a circle. Locate three points A, B, and C on the circle.
    2. Draw A B ¯ eh b bar  and B C ¯ . b c bar , .  Then construct the perpendicular bisectors of A B ¯ eh b bar  and B C ¯ . b c bar , .
    3. Reasoning Label the intersection of the two perpendicular bisectors as point O. What do you think is true about point O?

35. Two triangles are congruent if each side and each angle of one triangle is congruent to a side or angle of the other triangle. In Chapter 4, you will learn that if each side of one triangle is congruent to a side of the other triangle, then you can conclude that the triangles are congruent without finding the angles. Explain how you can use congruent triangles to justify the angle bisector construction.

    

Standardized Test Prep

SAT/ACT

36. What must you do to construct the midpoint of a segment?
    1. Measure half its length.
    2. Construct an angle bisector.
    3. Measure twice its length.
    4. Construct a perpendicular bisector.

37. Given the diagram below, what is NOT a reasonable name for the angle?

    

    6. ∠ ABC angle
    7. ∠ B angle b
    8. ∠ CBA angle
    9. ∠ ACB angle

Short Response

38. M is the midpoint of X Y ¯ . x y bar , .  Find the value of x. Show your work.

    

Mixed Review

See Lesson 1-5.

39. ∠ DEF angle  is the supplement of ∠ DEG angle  with m ∠ DEG = 64 . m angle  What is m ∠ DEF ? m angle
40. m ∠ TUV = 100 m angle  and m ∠ VUW = 80 . m angle  Are ∠ TUV angle  and ∠ VUW angle  a linear pair? Explain.

See Lesson 1-3.

Find the length of each segment.

41. A C ¯ eh c bar
42. A D ¯ eh d bar
43. C D ¯ c d bar

44. B C ¯ b c bar

    

Get Ready! To prepare for Lesson 1-7, do Exercises 45–47.

See p. 830.

Algebra Evaluate each expression for a = 6 eh equals 6  and b = − 8 . b equals negative 8 .

45. ( a − b ) 2 open eh minus b , close squared
46. a 2 + b 2 square root of eh squared , plus , b squared end root
47. a + b 2 fraction eh plus b , over 2 end fraction

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