C Challenge

37. A, B, and C are three noncollinear points. Describe and sketch a line in plane ABC such that points A, B, and C are equidistant from the line. Justify your response.
38. Reasoning M is the intersection of the perpendicular bisectors of two sides of Δ A B C . cap delta eh b c .  Line l is perpendicular to plane ABC at M. Explain why a point E on l is equidistant from A, B, and C. (Hint: See page 48, Exercise 33. Explain why Δ E A M ≅ Δ E B M ≅ Δ E C M . cap delta e eh m approximately equal to cap delta e b m approximately equal to cap delta e c m . )

Standardized Test Prep

SAT/ACT

39. For A(1, 3) and B(1, 9), which point lies on the perpendicular bisector of A B ¯ ? eh b bar , question mark
    1. (3, 3)
    2. (1, 5)
    3. (6, 6)
    4. (3, 12)
40. What is the converse of the following conditional statement? If a triangle is isosceles, then it has two congruent angles.
    6. If a triangle is isosceles, then it has two congruent sides.
    7. If a triangle has congruent sides, then it is equilateral.
    8. If a triangle has two congruent angles, then it is isosceles.
    9. If a triangle is not isosceles, then it does not have two congruent angles.
41. Which figure represents the statement B D ¯ b d bar  bisects ∠ A B C ? angle eh b c question mark
    1. 
    2. 
    3. 
    4. 

Short Response

42. The line y = 7 y equals 7  is the perpendicular bisector of the segment with endpoints A(2, 10) and B(2, k). What is the value of k? Explain your reasoning.

Mixed Review

See Lesson 5-1.

43. Find the value of x in the figure below.

    

See Lesson 1-5.

44. ∠ 1 angle 1  and ∠ 2 angle 2  are complementary and ∠ 1 angle 1  and ∠ 3 angle 3  are supplementary. If m ∠ 2 = 30 , m angle , 2 equals 30 , comma  what is m ∠ 3 ? m angle 3 question mark

Get Ready! To prepare for Lesson 5-3, do Exercises 45–47.

See Lesson 3-8.

45. What is the slope of a line that is perpendicular to the line y = − 3 x + 4 ? y equals . negative 3 x plus 4 . question mark
46. Line l is a horizontal line. What is the slope of a line perpendicular to l?
47. Describe the line x = 5 . x equals 5 , .

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