name class date geometry unit 3 practice · springboard geometry, unit 3 practice lesson 17-3 11....

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1© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 3 Practice

LeSSon 17-1 1. Find the image of each point after the

transformation (x, y) → x y

23

,32

.

a. (6, 6)

b. (12, 20)

c. (23, 10)

d.

13, 12

e. (0.15, 1.50)

2. Attend to precision. Quadrilateral A(23, 3), B(4, 5), C(6, 0), D(24, 24) is mapped onto

AʹBʹCʹDʹ by a dilation in which ABA B´ ´

23

5 .

The center of dilation is (0, 0).

x

25

25 5

y

5A (23, 3)

D(24, 24)

B (4, 5)

C (6, 0)

a. What is the scale factor for this dilation?

b. What are the coordinates of AʹBʹCʹDʹ?

3. Triangle X(1, 6), Y(5, 22), Z(25, 21) is mapped onto XʹYʹZʹ by a dilation with center (1, 22) and a scale factor of 3. Which function represents this dilation?

A. (x, y) → (x 1 3(x 1 1), y 1 3(y 1 2))

B. (x, y) → (x 1 3(x 2 1), y 1 3(y 2 2))

C. (x, y) → (x 1 3(x 2 1), y 1 3(y 1 2))

D. (x, y) → (x 1 3, y 2 6)

4. Make use of structure. In the diagram shown, a dilation maps each point (x, y) of the preimage PQR to (1 1 2(x 2 1), 22 1 2(y 1 2)).

25

25 5x

5

y

Q(24, 23)R (2, 24)

P (23, 4)

a. What is the scale factor?

b. Is the dilation an enlargement or a reduction?

c. What is the center of dilation?

d. What are the coordinates of the vertices of PʹQʹRʹ?

Geometry Unit 3 Practice

2

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© 2015 College Board. All rights reserved. SpringBoard Geometry, Unit 3 Practice

5. What are the coordinates of the image of rectangle ABCD after the figure undergoes a dilation with a scale factor of 0.75 centered at the origin?

x

y

25210

25

5

10

5 10

A (24, 10) B (4, 10)

C (4, 22)D (24, 22)

LeSSon 17-2 6. What single dilation produces the same image as

the composition o o o

D D D( ( )), 34

,40 ,4 ?

A. o

D, 3160

B. Do, 33 C. Do, 90 D. Do, 120

7. Model with mathematics. Write the sequence of similarity transformations that maps ABC to XYZ.

x

y

25210

210

25

5

10

5 10

A (26, 9)

B(26, 26 )

C (23, 26 )

Y(5, 22)Z (4, 22)

X (5, 3)

8. The sequence of similarity transformations below is applied to PQR to get STV.

(x, y) → (2x, 2y) → (2x, 3 2 2y)

What are the coordinates of the vertices of STV?

25

25 5x

5

y

R(1, 23)

P (23, 2) Q (1, 2)

9. A figure is transformed by the dilation Do , 14

and

then by another dilation. The composite of the two dilations is the same as the single dilation Do, 3. What is the second dilation?

10. Construct viable arguments. Is a dilation a rigid transformation? Explain your answer.

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LeSSon 17-3 11. Reason quantitatively. The two rectangles shown

are similar. What is the value of x?

2

16

4

x

12. Consider the two pairs of similar figures shown.

20

1210

z6

25

12

y

20

1210

z6

25

12

y

Find the values of y and z.

13. The vertices of a triangle are A(21, 4), B(4, 5), and C(6, 22). After a dilation with center (0, 0) and a scale factor of 3, the vertices are translated T(22, 5).

a. Is the image congruent to the original triangle? Is the image similar to the original triangle?

b. What are the vertices of AʹBʹCʹ, the final image?

14. Figure ABCD is similar to figure WXYZ. Which proportion CANNOT be used to find side lengths in the two figures?

A. ABWX

DAZW

5

B. ABBC

WXYZ

5

C. BCAD

XYWZ

5

D. CDAB

YZWX

5

15. Construct viable arguments. In isosceles ABC, AB 5 AC. AʹBʹCʹ is a dilation of ABC by a scale

factor of 12

.

a. Is AʹBʹCʹ isosceles? Explain.

b. What is the ratio of the perimeter of ABC to AʹBʹCʹ?

LeSSon 18-1 16. Reason quantitatively. Consider the triangles

shown. Are any of the triangles similar? Explain.

458 358

708

858

258

858

708

358

I

II

IIIIV

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17. Use triangles ABC and XYZ.

78.6°

78.6°

A

X

Y

Z

B

C

16

18

20

15

12

a. Show that ABC and XYZ are similar by the SAS similarity criterion.

b. Find YZ. Explain your steps.

c. Using the definition of similarity, explain why the two triangles are similar.

d. Complete this statement: BCA .

18. Which of the following is NOT an abbreviation for a statement that can be used to conclude that two triangles are similar?

A. AA similarity

B. SAS similarity

C. SSA similarity

D. ASA similarity

19. Construct viable arguments. Using the diagram shown, what information is needed to conclude that PQR PST using each criterion?

P

T

R

S

Q

a. AA similarity

b. SAS similarity

20. In the diagram shown, AB DE� and m∠ACB 5 35°.

16

18

A

BC D

E

358

a. If m∠A 5 (5x 1 3)° and m∠B 5 (15x 1 2)°, find m∠D and m∠E.

b. If AC 5 20, find EC to the nearest tenth.

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LeSSon 18-2 21. Reason quantitatively. In the diagram shown,

RS XY� , m∠X 5 25°, XY 5 30, RS 5 26, and ZY 5 20.

X

R

Z SY

a. What is m∠SRZ?

b. Complete this statement: ∠ZYX .

c. What is the value of the ratio XZRZ

expressed as a reduced fraction? Expressed as a decimal to the nearest hundredth?

d. If ZY 5 20, what is SY to the nearest hundredth?

e. If XR 5 2, find RZ and XZ.

22. Find DE in the diagram shown. Write your answer as a decimal rounded to the nearest tenth.

A

C B

D

FE 1014

11

A

C B

D

FE 1014

11

23. Triangle I has side lengths 8, 9, and 6 units.

Triangle II has side lengths 8 units, 1023

units, and

12 units. Show that the two triangles are similar.

24. Persevere in solving problems. The length of the sides of Triangle I are 6 units, 10 units, and 8 units. One side of Triangle II has a length of 12 units.

a. Find the lengths of the other two sides of Triangle II if the sides with lengths 6 units and 12 units are corresponding sides.

b. Find the other two lengths in Triangle II if the sides with lengths 10 units and 12 units are corresponding sides.

c. Find the other two lengths in Triangle II if the sides with lengths 8 units and 12 units are corresponding sides.

d. Triangle III is similar to the other two triangles, and its longest side has a length of 3 units. What are the lengths of the other two sides of Triangle III?

25. In the diagram shown, ⊥AB BC, ⊥BD AC, and ∠A ∠CBD. Therefore, the two small triangles are similar to each other, and to the large triangle, by AA similarity. Which proportion is NOT true?

B

A D C

A. ACBC

BCDC

5

B. DBDA

DCDB

5

C. ABAD

ACAB

5

D. ADAB

DCBC

5

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LeSSon 18-3 26. In the diagram shown, �DE FG. Which proportion

is NOT true?

D

EH

F

G

A. HFHD

FGDE

5

B. HEHG

HDHF

5

C. DEFG

HDDF

5

D. FDDH

GEEH

5

27. Make use of structure. Use the diagram shown to write a proportion to illustrate the Triangle Proportionality Theorem.

XV

Y

a

d W c

b

Z

28. In the diagram shown, ED CB� .

A

B

C

E

30 m

25 m

D

75 m

a. Complete this statement using segments from the diagram: 30

25 5 .

b. Find AD and DB, each to the nearest tenth.

29. Reason quantitatively. In the diagram shown, � �XY ZW QR. Use the given measurements to

find each length.

P

10

10.530 14

16

36Q

X

Z

R

Y

W

a. PX

b. XQ

c. XY

d. ZW

30. In the diagram shown, CD 5 7, DB 5 8, AE 5 5, and m∠C 5 62°.

5

A

E

C 7 8 BD

62° x °

a. If AC DE� , what is AB?

b. If AC DE� , what is the value of x?

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LeSSon 19-1 31. In the diagram shown, ⊥SP PT and ⊥PM ST .

P

MS T

a. Name two angles that are congruent to ∠SMP.

b. Name an angle that is congruent to ∠SPM.

c. Name an angle that is congruent to ∠S.

d. How many right triangles appear in the diagram?

32. Make sense of problems. This diagram shows a rectangle ACJG and its two diagonals. Points B, F, H, and D are midpoints of the sides.

H

BA C

FE

D

G J

a. Which segment is an altitude of ACE?

b. Which segment is an altitude of CGJ?

c. Which segment is an altitude of CEJ?

d. Which triangles have AG as an altitude?

33. Attend to precision. In the diagram shown, ⊥SP PT , ⊥PM ST , PS 5 13, and SM 5 5.

P

5

13

S MT

a. Find PM.

b. Find MT.

c. Find ST.

d. Find PT.

34. In DEF, DE 5 DF and DG is a segment from vertex D. Which of the following statements is NOT true?

D

E

G

F

A. If DG is a median in isosceles triangle DEF, then DG forms two right triangles.

B. If DG is an angle bisector in isosceles triangle DEF, then DG forms two right triangles.

C. If G is a point on EF , then DG forms two right triangles.

D. If DG is a perpendicular bisector of EF , then DG forms two right triangles.

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35. Write a similarity statement comparing the three triangles in the diagram shown.

K

M

L

J

LeSSon 19-2 36. Use the segments in the diagram shown. Which

proportion does NOT represent Corollary 1 or Corollary 2 of the Right Triangle Altitude Theorem?

a b

cd

e

A. a b c

ac1

5

B. ad

db

5

C. cd

de

5

D. a be

eb

15

37. express regularity in repeated reasoning. Use the diagram shown. If necessary, round your answers to the nearest tenth.

t

m

n

a. Find t if m 5 2 and n 5 8.

b. Find m if t 5 5 and n 5 6.

c. Find m 1 n if t 5 4 and n 5 4.

d. Find t if m 5 4 and m 1 n 5 13.

38. Use the diagram shown. If necessary, round your answers to the nearest tenth.

sp

r

q

a. Find q if r 5 4 and s 5 12.

b. Find r if q 5 10 and r 1 s 5 50.

c. Find s if q 5 8 and r 5 3.

d. Find p if r 5 s 5 6 and q 5 8.

39. Determine the positive geometric mean of each pair of values. Simplify any radicals.

a. 25 and 100

b. 27 and 36

c. 1 and 45

d. 100 and 200

e. a and b

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40. Persevere in solving problems. In the diagram shown, ⊥BC CA and ⊥CD BA .

4 16

a bf

d e

C

AD

B

c

a. Use a corollary of the Right Triangle Altitude Theorem to find f.

b. Use the base AB and altitude CD to find the area of ABC. Show your work.

c. Use a corollary of the Right Triangle Altitude Theorem to find a and b.

d. Using a and b as the base and height of ABC, find the area of ABC. Show your work.

e. What do you notice about your answers to Parts b and d?

LeSSon 20-1 41. Which three numbers do NOT form a Pythagorean

triple?

A. 5, 12, 13

B. 6, 8, 10

C. 6, 10, 14

D. 8, 15, 17

42. A supporting wire is attached to a tree at a height of 45 feet from the ground. If the length of the wire is 51 feet, what is the distance between the base of the tree and the foot of the wire?

45 ft

51 ft

wire

?

43. Attend to precision. The length of a rectangular rug is 18 feet and the length of its diagonal is 22 feet.

18 ft

22 ft

a. What is the width of the rug, to the nearest foot?

b. What is the perimeter of the rug, to the nearest foot?

c. What is the area of the rug, to the nearest square foot?

d. A second rectangular rug has side lengths that are the same as the width and diagonal of the original rug. What is the length of the diagonal of the second rug to the nearest foot?

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44. Reason quantitatively. An isosceles triangle has side lengths 15 units, 15 units, and 8 units.

15 15

8

h

a

a. What is the length of the altitude h from the vertex angle, to the nearest tenth?

b. What is the area of the triangle, to the nearest tenth?

c. What is the length of the altitude a from one of the base angles?

d. Find the sum of the lengths of the three altitudes of the triangle.

45. Two sides of a right triangle have lengths 15.1 cm and 30.6 cm.

a. Find the length of the third side if the given lengths represent the legs of the triangle.

b. Find the length of the third side if the given lengths represent the hypotenuse and one leg of the triangle.

LeSSon 20-2 46. Tell whether the three lengths are the sides of an

acute triangle, a right triangle, or an obtuse triangle.

a. 8, 11, 12

b. 24, 45, 51

c. 310

, 25, 12

d. 12, 14, 20

e. 9, 11, 13

47. Construct viable arguments. Tell whether or not each triangle is a right triangle. Explain your answers.

a.

15.1

18.4

23.8

b.

18.5 11.3

13.5

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48. Reason quantitatively. Two sides of a triangle are 8.6 cm and 10.5 cm.

a. What is an inequality that represents the length s of the shortest side of the triangle?

b. What is an inequality that represents the length l of the longest side of the triangle?

c. What is the length of the third side if it is the leg of a right triangle?

d. What is the length of the third side if it is the hypotenuse of a right triangle?

49. Four students wrote the following statements about two given positive numbers. Which statement is always true?

A. If I select any number between the two given numbers, the three numbers can be the sides of a right triangle.

B. If the two numbers are the lengths of two sides of a triangle, then the sum of the two numbers can be the length of the third side of the triangle.

C. If I select any number between the two given numbers, the three numbers can be the lengths of the sides of a triangle.

D. If the two numbers are lengths of two sides of a triangle, the length for the third side can be any one of these three choices: it can be less than the sum of the two numbers, it can be greater than the difference of the two numbers, or it can be between the two numbers.

50. For Parts a–e, the last number represents the length of the hypotenuse of a right triangle and the other two numbers represent the lengths of the legs. Find each missing length.

a. 10 , ? , 15

b. 8 , ? , 10

c. 100 , ? , 101

d. 19 , ? , 25

e. n , ? , n 31

LeSSon 21-1 51. Use appropriate tools strategically. Find the

length of the hypotenuse of an isosceles right triangle given the length of a leg. Write each answer as an exact value and as a decimal rounded to the nearest hundredth.

a. 12 in.

b. 25 cm

c. 7a ft

d. ab

units

52. Find the length of the leg of an isosceles right triangle given the length of a hypotenuse. Write each answer as an exact value and as a decimal rounded to the nearest hundredth.

a. 22 in.

b. 19 cm

c. 5a ft

d. cd

units

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53. In an isosceles right triangle, the length of the hypotenuse is 8 units. Which measurement is NOT associated with the triangle?

A. 4 2 units

B. 8 2 units

C. 45°

D. 90°

54. Find the length in each isosceles right triangle.

a. Find the leg if the hypotenuse is 6 2 units.

b. Find the hypotenuse if the leg is 13 2 cm.

c. Find the hypotenuse if the leg is (1 1 3) cm.

d. Find the leg if the hypotenuse is 12

unit.

55. Make sense of problems. For an isosceles right triangle, find the length of the leg and the hypotenuse with the given criterion.

a. The perimeter is (14 1 7 2 ) units.

b. The perimeter is (20 1 10 2 ) units.

c. The area is 12.5 square units.

d. The area is m2

square units.

LeSSon 21-2 56. express regularity in repeated reasoning. Find

the length of the longer leg and the length of the hypotenuse given the length of the shorter leg of a 30°-60°-90° triangle.

a. 15 in.

b. 8 3 cm

c. a ft

d. 3 5 units

57. Find each length for a 30°-60°-90° triangle.

a. the shorter leg and the longer leg if the hypotenuse is 25 cm

b. the shorter leg and the hypotenuse if the longer leg is 12 in.

c. the shorter leg and the hypotenuse if the longer leg is 10 ft

d. the shorter leg and the longer leg if the

hypotenuse is 23

units

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58. In a 30°-60°-90° triangle, one of the legs has a length of 30 cm. Which of the following measurements is NOT associated with this triangle?

A. 10 3

B. 20 3

C. 30 3

D. 60 3

59. In a 30°-60°-90° triangle, find the lengths of the legs and the hypotenuse with the given criterion.

a. The perimeter of the triangle is (15 1 5 3 ) cm.

b. The area is 36 3 square units.

c. The triangle is half of an equilateral triangle with sides that measure 30 units.

d. The perimeter is (3a 1 a 3 ) units.

60. Make use of structure. Find a, b, c, and d in the diagram shown.

P

S

Q

a

b

c

d

5

R

608

LeSSon 22-1 61. Model with mathematics. Identify the indicated

side in the right triangle shown.

M

TN

a. the leg that is opposite angle N

b. the leg that is adjacent to angle M

c. the leg that is adjacent to angle N

d. the leg that is opposite angle M

62. Find the indicated measures in the triangle shown.

R S

Q

61.98

8

17

a. QS

b. m∠S

c. Draw and label a triangle XYZ so XYZ QRS and the scale factor from QRS to XYZ is 7 : 2. Indicate the measures of all sides and angles.

d. Explain how you found the measures of the sides and angles of XYZ.

63. In a right triangle, the hypotenuse is 15 cm and a leg is 11 cm. In a similar right triangle, the hypotenuse is 9 cm. Find the lengths of the legs of the smaller triangle. Write your answers to the nearest tenth.

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64. Right triangle DEF is similar to right triangle HJK. DEF is larger than HJK, and the length of HK is 7.5 cm. Which statement describes how to calculate the length of DF?

A. Add 7.5 to the length of HK .

B. Subtract 7.5 from the length of HK .

C. Multiply the length of HK by 7.5.

D. Divide the length of HK by 7.5.

65. Make use of structure. Find the scale factor and the unknown angle measures and side lengths for the pair of similar right triangles shown.

A

B

F D

E

817

C

61.98 28.18

6

A

B

F D

E

817

C

61.98 28.18

6

LeSSon 22-2 66. Model with mathematics. Use the triangle shown

to write a fraction for each trigonometric ratio.

P Q

R

r

pq

a. sin P

b. tan Q

c. cos Q

d. sin Q

e. tan P

67. Using the triangle shown, write each ratio in simplest form.

M N

T

55 73

48

a. tan N

b. tan T

c. sin T

d. cos T

e. sin N

68. Use appropriate tools strategically. Use a calculator to find each value. Round your answers to the nearest hundredth.

a. sin 57.3°

b. cos 42.8°

c. tan 89.6°

d. cos 90°

e. tan 45°

69. Which trigonometric ratio can be greater than 1?

A. sine

B. cosine

C. tangent

D. all three ratios

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70. Which statement is NOT true?

A. sin 45° 5 cos 45°

B. sin 20° 1 sin 50° 5 sin 70°

C. cos 74.7° 5 sin 15.3

D. sin 35° 5 cos 55°

LeSSon 22-3 71. Use trigonometric ratios to find the indicated side

lengths in the diagram shown. Show your work and write your answers to the nearest tenth.

M

P N

a

b

688

150

a. a

b. b

72. Use appropriate tools strategically. Find the perimeter and area of each triangle. Show your work.

a. m

6287

27.6

b.

q

p

438

17.8

73. In right triangle XYZ, m∠Y 5 37° and XY 5 27. Which of the following is NOT a method you can use to find XZ?

A. Solve sin Y 5 yz .

B. Solve tan Y 5 yx .

C. Solve cos Y 5 xz , and then use the Pythagorean Theorem.

D. Find m∠X, and then solve cos X 5 yz .

74. Use appropriate tools strategically. The diagonal of rectangle ABCD is 42.3 cm, and it forms an angle of 53° with the shorter side AD of the rectangle.

A

D

T

C

B

538

42.3 cm

a. Find the length and width of the rectangle. Show your work.

b. Use the area of ABD to find the length of AT , the altitude from vertex A in ABD. Show your work.

c. Use a trigonometric ratio in ADT to find AT.

d. Compare your results for Parts b and c. Which method do you prefer?

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75. A campsite at point P is 600 meters from a river. One group of campers hikes to the river on a path that forms a 68° angle with the direct route to the river, and gets to the river at point A. Another group of campers hikes to the river at a path that forms a 40° angle with the direct path to the river, and gets to the river at point B.

A BR

P

River

600 m

688408

a. What is the length of the path from P to A?

b. What is the length of the path from P to B?

c. How far apart are points A and B?

d. How much longer is the distance from A to P to B than the straight-line distance from A to B?

LeSSon 22-4 76. Use appropriate tools strategically. Use a

calculator to find each angle measure. Be sure your calculator is in degree mode.

a. sin A 5 0.5736

b. tan D 5 0.9657

c. cos B 5 0.1994

d. tan21 (4.0108)

e. sin21

1517

77. Model with mathematics. A ramp is being designed so that wheelchairs can go up the distance AB, which is 2.5 feet. Write each answer to the nearest hundredth of a degree.

A

BC

2.5 ft

a. If CB is 30 feet, what is the measure of ∠ACB?

b. If CA is 30 feet, what is the measure of ∠ACB?

78. Find all the missing sides and angles for the triangle shown.

A

BC

16

418

79. Find the missing sides and angles for the triangle shown.

D

25

23

EF

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80. For the right triangle shown, which statement is NOT true?

ac

b

x8

A. x 5 90 2 tan21

ba

B. x 5 tan21

ab

C. x 5 cos21

bc

D. x 5 cos21

ac

LeSSon 23-1 81. Construct viable arguments. Complete the steps

below to derive a part of the Law of Sines.

P

Q T

rq

p

h

R

a. In PQT, write an expression for sin Q.

b. In PRT, write an expression for sin R.

c. Solve for h in Parts a and b.

d. In Part c, there are two expressions for h. Set them equal to each other.

e. Starting with your equation in Part d, divide each side by rq.

82. Write the three-part statement of the Law of Sines for the triangle shown.

M

N

T

n

m

t

83. Use appropriate tools strategically. Find each measure to the nearest tenth.

U

V

W

838

15.2

588

a. VW

b. UV

84. The Law of Sines CANNOT be applied to which of the following?

A. acute triangles

B. obtuse triangles

C. right triangles

D. triangles where no angle measures are known

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85. Which measure for ABC can be found using the Law of Sines?

17.8

13

A

B

C

1058

A. AC

B. the altitude from vertex A

C. m∠C

D. m∠B

LeSSon 23-2 86. Which diagram indicates two sides and the

nonincluded angle?

A.

B.

C.

D.

87. Consider the triangles below.

P

RQ T V

S

1212

15 15

388 388

a. Use the Law of Sines in PQR to find m∠Q. Show your work.

b. Use the Law of Sines in STV to find m∠T. Show your work.

c. Compare your answers to Parts a and b with the triangles in the illustration. What do you conclude?

d. How can you find the actual measure of ∠T in STV?

88. Consider DEF with m∠F 5 40°, DF 5 32, and DE 5 25. Find two possible values, each to the nearest whole number, for each expression.

a. m∠E

b. EF

89. Make sense of problems. Sketch two possibilities for WXY if m∠W 5 45°, YW 5 10, and YX 5 8.

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90. Reason quantitatively. Use your triangles from Item 89, where m∠W 5 45°, YW 5 10, and YX 5 8.

a. Find the two possible values for m∠Y, each to the nearest tenth.

b. Find the two possible values for XW, each to the nearest tenth.

LeSSon 23-3 91. Which one of the following is a statement of the

Law of Cosines for PRQ?

P

Q

R

p

r

q

A. p2 5 q2 1 r2 2 2pq cos P

B. q2 5 p2 1 r2 1 2pr cos Q

C. r2 5 p2 1 q2 2 2pq cos R

D. r2 5 p2 1 q2 2 2rp cos P

92. Use appropriate tools strategically. Consider MNT. Find m∠N to the nearest tenth of a degree.

M

N

T26.1 cm

15.7 cm

14.8 cm

93. Which set of known measures is NOT enough to use the Law of Cosines?

A. the three sides of the triangle

B. two sides and one angle of the triangle

C. two sides and three angles of the triangle

D. one side and two angles of the triangle

94. Attend to precision. Consider the triangle shown. Find YZ to the nearest tenth.

Y

X

Z

23.5 cm

11.2 cm

418

95. In an isosceles triangle, the legs are 12 cm and the base is 5 cm.

a. Find the measure of the vertex angle.

b. Find the measure of the base angles.

LeSSon 23-4 96. Suppose you know the measures of three parts of a

triangle. Which combination of known sides and angles is NOT sufficient to let you use the Law of Sines to find other parts of the triangle?

A. the length of two sides and the measure of an angle opposite one of the sides

B. the measures of three sides of the triangle

C. the measures of two angles and the length of the side between the angles

D. the measures of two angles and the length of a side that is not between the angles

20

Name class date


97. Consider triangle PQR.

Q

P

R

11.7

12.3

9.5

a. What combinations of sides and angles are shown?

b. Which law can you use to find another measurement, the Law of Sines or the Law of Cosines?

c. What is m∠P to the nearest tenth?

d. What is m∠Q to the nearest tenth?

e. What is m∠R to the nearest tenth?

98. Consider triangle DEF.

D

F E

13.2

1128 428



c. What is DE to the nearest tenth?

d. What is FE to the nearest tenth?

e. What is m∠D to the nearest tenth?

99. Make use of structure. Consider triangle HJK.

K J23.9

18.7

H

938



c. What is HK to the nearest tenth?

d. What is m∠K to the nearest tenth?

e. What is m∠H to the nearest degree?

100. Attend to precision. Two surveyors at points A and B are exactly 100 meters apart. The diagram shows the angle measures from the surveyors to their supply truck at point T.

A B

T

100 m258 298

Which surveyor is closer to the supply truck? How much closer (to the nearest tenth)? Show your work.

name class date geometry unit 3 practice · springboard geometry, unit 3 practice lesson 17-3 11....

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