iblog.dearbornschools.org · Web view____42.Michele wanted to measure the height of her...

Similarity Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model?a. 1 : 18 b. 18 : 1

____ 2. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower?a. 725 : 1 b. 1 : 725

____ 3. The length of a rectangle is 61

2 inches and the width is 33

4 inches. What is the ratio, using whole numbers, of the length to the width?a. 26 : 15 b. 26 : 30

____ 4. If then 3a = ____.a. 5b b. 3b

____ 5. If , which equation must be true?a. b.

____ 6. If , then = ____.a. b.

Solve the proportion.

____ 7.a. 81 b. 9

____ 8.a. 5 b. 25

____ 9.a. –3 b. 3

____ 10.a. b.

____ 11. A map of Australia has a scale of 1 cm to 120 km. If the distance between Melbourne and Canberra is 463 km, how far apart are they on the map, to the nearest tenth of a centimeter?a. 38.6 cm b. 3.9 cm

____ 12. On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long and 4 cm wide on the blueprint?a. 6 ft b. 22.5 ft

____ 13. You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your scale drawing?a. 16 in. by 10 in. b. 24 in. by 144 in.

____ 14. A model is built having a scale of 1 : 100,000. How high would a 35,600-ft mountain be in the model? Give your answer to the nearest tenth of an inch.a. 4.272 in. b. 0.356 in.

____ 15. Solve the extended proportion for x and y with x > 0 and y > 0.a. x = 6; y = 6 b. x = 3; y = 12

____ 16. . Complete the statements.

D C

E B

A

J

H

G

F

a.

b.ABGH

DJ

a. E; DC b. ; DC

____ 17. Figure . Name a pair of corresponding sides?

a. b.

____ 18. The two rectangles are similar. Which is a correct proportion for corresponding sides?

x

8 m4 m

12 m

a. b.

____ 19. Determine whether the figures are similar.

6.6

3

1.9

6.6

3

1.9

6.086.08

Not drawn to scale

a. similarb. not similar

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

____ 20. In RST, RS = 10, RT = 15, and mR = 32. In UVW, UV = 12, UW = 18, and mU = 32.a.

;

c.

; b.

;

d. The triangles are not similar.

____ 21. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.a.

;

c.

; b.

;

d. The triangles are not similar.

____ 22. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.

A

B

D

CW

X

Z

Z

a. 29.5 b. 177

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.

____ 23.a.

x = 9, y =

b. x = 9, y = 27

____ 24. The pentagons are regular.

164

6

8x – 3 y – 2

a. x = 27, y = 5 b. x = 27, y = 4____ 25. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

A

B C

D

FE

4

55x

x

a. AB = 10; EF = 2 b. AB = 4; EF = 20____ 26. You want to draw an enlargement of a design that is printed on a card that is 4 in. by 5 in. You will be

drawing this on an piece of paper that is in. by 11 in. What are the dimensions of the largest complete enlargement you can make?a. 13

5 in. 43

8 in.b.

1058 in.

____ 27. You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page?a. b.

____ 28. An artist’s canvas forms a golden rectangle. The longer side of the canvas is 33 inches. How long is the shorter side? Round your answer to the nearest tenth of an inch.

a. 16.5 in. b. 20.4 in.____ 29. If the long side of a golden rectangle is 36 cm, what is its area? Round your answer to the nearest tenth.

a. 801 cm b. 2096.9 cm____ 30. If one measurement of a golden rectangle is 8.8 inches, which could be the other measurement?

a. 14.238 in. b. 7.182 in.____ 31. Write a similarity statement for the triangles.

60° 60°

53°

67°

C E F H

D

G

a. b.____ 32. Are the triangles similar? If so, explain why.

84.6° 84.6°

30.4°

65°

a. yes, by SAS b. yes, by AA

____ 33. What is the measure of ?

Q S

R

T V

UU)

)

)) ))63°

47°

a. 110 b. 70____ 34. Which group contains triangles that are all similar?

a.

b.

) )45° 45° 7

7 7

) )53° 53°

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

____ 35. In QRS, QR = 16, RS = 64, and mR = 29. In UVT, VT = 8, TU = 32, and mT = 29.a. ; ASA c. ; ASAb. ; ASA d. The triangles are not similar.

____ 36.

A

B

C

5 5

8

O M

7.5

12

N

7.5

a. ; SSS c. ; AAb. ; SAS d. The triangles are not similar.

____ 37.a. ; SAS c. ; SSSb. ; SAS d. The triangles are not similar.

Explain why the triangles are similar. Then find the value of x.

____ 38.

12

8

x

7

Not drawn to scale

)

)

a.SAS Postulate;

423

b.AA Postulate;

423

____ 39.

x

6

4

8

Not drawn to scale

>

>

a.AA Postulate;

1313

b.AA Postulate;

513

____ 40. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale.

a. 73.8 m b. 42.3 m____ 41. Use the information in the diagram to determine the height of the tree to the nearest foot.

a. 80 ft b. 72 ft____ 42. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet

from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

a. 25 ft b. 20 ft

Find the geometric mean of the pair of numbers.

____ 43. 175 and 7a. 55 b. 35

____ 44. 5 and 6a. 30 b. 30

Solve for a and b.

____ 45.

)

)

10

8

6 a

b

a. b.

____ 46.

)

)

29

21

20 a

b

a. b.

____ 47. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

5 26

a. 130 b. 31

____ 48. Jason wants to walk the shortest distance to get from the parking lot to the beach.

ParkingLot

RefreshmentStand

30 m

40 m40 m

Beach

a. How far is the spot on the beach from the parking lot?b. How far will his place on the beach be from the refreshment stand?

a. 24 m; 18 m b. 24 m; 32 m

____ 49. Use the Side-Splitter Theorem to find x, given that .

B

A

C

P Q8

x 18

12

a. 12 b. 6

____ 50. Given: . Find the length of . The diagram is not drawn to scale.

B

A

C

P Q6

12 18

a. 11 b. 9

____ 51. Given , solve for x.The diagram is not drawn to scale.

E C

A

D

B

5 7

11

x

a. b.

____ 52. Find the values of x and y, given that .

M

OP

y

x9

1820

N

Q

a. x = 10; y = 25.5 b. x = 25.5; y = 10

Solve for x.

____ 53.

x

x + 5 x + 1

x – 2

>

>

a. 7.5 b. 5

____ 54.

24 36

12x>

>

>

a. 8 b. 2

____ 55.

3x 3x + 7

5x – 84x>

>

>

a. b.

____ 56.

4 5

x

Not drawn to scale

a. 6 b. 2 5

____ 57.7 13

x

a. b.

____ 58. bisects , LM = 18, NO = 4, and LN = 10. Find OM.

L

N

M

O

a. 45 b. 7.2____ 59. Find x to the nearest tenth.

x

Not drawn to scale

))))

8.3

6.7

11.6

a. 1.7 b. 14.4

____ 60. Four explorers are trying to find the distance across an oddly shaped lake. They position themselves as shown in the diagram. Alhombra uses her compass to instruct Chou and Duong to move along the line they form with Bizet until she sees that from her perspective the angle between Bizet and Chou is equal to the angle formed between Chou and Duong. They measure the distance between Bizet and Chou to be 35 m, between Chou and Duong to be 46 m, and between Alhombra and Duong to be 100 m. How long is the lake from east to west? Round your answer to the nearest tenth of a meter.

a. 132.4 m b. 76.1 m____ 61. An angle bisector of a triangle divides the opposite side of the triangle into segments 8 cm and 4 cm long. A

second side of the triangle is 4.4 cm long. Find all possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter.a. 35.2 cm, 7.3 cm b. 8.8 cm, 2.2 cm

Essay

62. Write a proof.Given: Prove:

A

E

D

C

B

Similarity ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 1 KEY: ratio | word problem

2. ANS: B PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 1 KEY: ratio | word problem

3. ANS: A PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 1 KEY: ratio

4. ANS: A PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 2 KEY: proportion | Cross-Product Property

5. ANS: A PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 2 KEY: Cross-Product Property | proportion

6. ANS: A PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 2 KEY: Cross-Product Property | proportion

7. ANS: B PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 3 KEY: proportion | Cross-Product Property

8. ANS: B PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 3 KEY: proportion | Cross-Product Property



11. ANS: B PTS: 1 DIF: L1 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-1 Example 4 KEY: proportion | Cross-Product Property | word problem

24. ANS: B PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 3 KEY: corresponding sides | proportion

25. ANS: A PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 3 KEY: corresponding sides | proportion | similar polygons

26. ANS: B PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 4 KEY: similar polygons | word problem

27. ANS: A PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 4 KEY: similar polygons | word problem

28. ANS: B PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 5 KEY: similar polygons

29. ANS: A PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 5 KEY: golden rectangle | area

30. ANS: A PTS: 1 DIF: L1 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 5 KEY: golden rectangle

31. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 1KEY: Angle-Angle Similarity Postulate

32. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 2KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem

33. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 1KEY: Angle-Angle Similarity Postulate | corresponding angles

34. ANS: A PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 2KEY: Angle-Angle Similarity Postulate | Side-Angle-Side Similarity Theorem | Side-Side-Side Similarity Theorem

35. ANS: D PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 2KEY: corresponding sides

36. ANS: A PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 2KEY: Side-Side-Side Similarity Theorem

37. ANS: A PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 2KEY: Side-Angle-Side Similarity Theorem | corresponding sides

38. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 3KEY: Angle-Angle Similarity Postulate

39. ANS: A PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 3KEY: Angle-Angle Similarity Postulate

40. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 4KEY: Side-Angle-Side Similarity Theorem | word problem

41. ANS: A PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 4KEY: Angle-Angle Similarity Postulate | word problem

42. ANS: B PTS: 1 DIF: L1 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-3 Example 4KEY: Angle-Angle Similarity Postulate | word problem

43. ANS: B PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 1KEY: geometric mean | proportion

44. ANS: A PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 1KEY: geometric mean | proportion

45. ANS: B PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 2KEY: corollaries of the geometric mean | proportion

46. ANS: A PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 2KEY: corollaries of the geometric mean | proportion

47. ANS: A PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 2KEY: corollaries of the geometric mean | proportion

48. ANS: B PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right Triangles

NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 TOP: 7-4 Example 3KEY: corollaries of the geometric mean | multi-part question | word problem

49. ANS: A PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 1KEY: Side-Splitter Theorem

50. ANS: B PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 1KEY: Side-Splitter Theorem



53. ANS: B PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 1KEY: Side-Splitter Theorem

54. ANS: A PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 2KEY: corollary of Side-Splitter Theorem

55. ANS: A PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 2KEY: corollary of Side-Splitter Theorem

56. ANS: A PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-4 Example 2KEY: corollaries of the geometric mean | proportion

57. ANS: B PTS: 1 DIF: L1 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-4 Example 2KEY: corollaries of the geometric mean | proportion

58. ANS: B PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.2 Using the Triangle-Angle-Bisector TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 3KEY: Triangle-Angle-Bisector Theorem


60. ANS: B PTS: 1 DIF: L1 REF: 7-5 Proportions in TrianglesOBJ: 7-5.2 Using the Triangle-Angle-Bisector TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 3KEY: Triangle-Angle-Bisector Theorem | word problem


ESSAY

62. ANS:[4] Answers may vary. Sample:

1. Given2. Prop. of Proportions

3. Vertical are .4. SAS Theorem

[3] correct steps but with minor error in reasons[2] error in steps

[1] error in steps and reasons

PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3KEY: extended response | rubric-based question | Property of Proportions | vertical angles | Side-Angle-Side Similarity Theorem

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