49. State the converse of the Triangle-Angle-Bisector Theorem. Give a convincing argument that the converse is true or a counterexample to prove that it is false.
50. In △ A B C , white up pointing triangle eh b c comma  the bisectors of ∠ A , angle eh comma   ∠ B , angle b comma  and ∠ C angle c  cut the opposite sides into lengths a 1 eh sub 1  and a 2 , b 1 eh sub 2 , comma . b sub 1  and b 2 , b sub 2 , comma  and c 1 c sub 1  and c 2 , c sub 2 , comma  respectively, labeled in order counterclockwise around △ A B C . white up pointing triangle eh b c .  Find the perimeter of △ A B C white up pointing triangle eh b c  for each set of values.
    1. b 1 = 16 , b sub 1 . equals 16 comma   b 2 = 20 , b sub 2 . equals 20 comma   c 1 = 18 c sub 1 , equals 18
    2. a 1 = 5 3 , a 2 = 10 3 , b 1 = 15 4 eh sub 1 , equals , 5 thirds , comma , eh sub 2 , equals , 10 over 3 , comma , b sub 1 , equals , 15 over 4

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

51. What is the value of x in the figure below?

    

52. Suppose △ V L Q ∼ △ P S X . white up pointing triangle v l q , tilde operator white up pointing triangle p s x .  If m ∠ V = 48 m angle , v equals 48  and m ∠ L = 80 , m angle , l equals 80 , comma  what is m ∠ X ? m angle x question mark

53. In the diagram below, P R ¯ ≅ Q R ¯ . p r bar , approximately equal to , q r bar , .  For what value of x is T S ¯ t s bar  parallel to Q P ¯ ? q p bar , question mark

    

54. Leah is playing basketball on an outdoor basketball court. The 10-ft pole supporting the basketball net casts a 15-ft shadow. At the same time, the length of Leah's shadow is 8 ft 3 in. What is Leah's height in inches? You can assume both Leah and the pole supporting the net are perpendicular to the ground.

Mixed Review

See Lesson 7-4.

Use the figure to complete each proportion.

55. n h = h □ n over h , equals , fraction h , over white square end fraction
56. □ b = b c fraction white square , over b end fraction , equals , b over c
57. n a = a □ n over eh , equals , fraction eh , over white square end fraction
58. m h = □ n m over h , equals , fraction white square , over n end fraction

See Lesson 5-3.

Find the center of the circle that you can circumscribe about each △ A B C . white up pointing triangle eh b c .

59. A(0, 0)

    B(6, 0)

    C ( 0 , − 6 ) c open 0 comma negative 6 close

60. A(2, 5)

    B ( − 2 , 5 ) b open minus , 2 comma 5 close

    C ( − 2 , − 1 ) c open minus , 2 comma negative 1 close

61. A ( − 2 , 0 ) eh open minus , 2 comma 0 close

    B(5, 5)

    C ( − 2 , 5 ) c open minus , 2 comma 5 close

Get Ready! To prepare for Lesson 8-1, do Exercises 62–64.

See p. 829.

Square the lengths of the sides of each triangle.

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