Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry M2 Unit 1 Practice Exam

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. 18 : 1 b. 1 : 18 c. 9 : 6 d. 6 : 9

____ 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. 1 : 725 b. 725 : 1 c. 12 : 725 d. 725 : 12

____ 3. The length of a rectangle is 612

inches and the width is 414

inches. What is the ratio, using whole numbers, of

the length to the width?a. 13 : 17 b. 26 : 34 c. 17 : 26 d. 26 : 17

____ 4. Red and grey bricks were used to build a decorative wall. The number of red bricksnumber of grey bricks

was 52

. There were

175 bricks used in all. How many red bricks were used?a. 25 c. 50b. 125 d. 35

____ 5. The measure of two complementary angles are in the ratio 1 : 4. What are the degree measures of the two angles?a. 45° and 135° c. 36° and 144°b. 23° and 68° d. 18° and 72°

____ 6. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the rectangle?a. 32 feet c. 64 feetb. 48 feet d. 96 feet

____ 7. A salsa recipe uses green pepper, onion, and tomato in the extended ratio 2 : 5 : 10. How many cups of onion are needed to make 204 cups of salsa?a. 24 c. 60b. 5 d. 120

____ 8. The measures of the angles of a triangle are in the extended ratio 2 : 3 : 5. What is the measure of the smallest angle?a. 18 c. 90b. 54 d. 36

What is the solution of each proportion?

____ 9. 6

a

18

27a. 54 b. 81 c. 9 d. 18

Name: ________________________ ID: A

2

____ 10. 79

m27

a.121

b. 21 c. 3 d.73

____ 11. n 6

3n

n 5

3n 1

a. –3 b.2

5c.

9

17d. 3

____ 12. 3y 8

12

y

5

a. 10 b. 7 c.3

40d.

40

3

____ 13. Given the proportion ab

815

, what ratio completes the equivalent proportion a8 ?

a.15b

c.815

b.b15

d.a15

____ 14. Figure TQRS BCDE. What are the pairs of congruent angles?

a. R D,

Q E,

T B, and

S C

b. R D,

S B,

Q C, and

T E

c. S D,

R E,

T B, and

Q C

d. R D,

S E,

T B, and

Q C

Name: ________________________ ID: A

3

____ 15. ABCDE GHJDF. Complete the statements.

a. H

b.

a. B; DC b. E; AE c. E; DC d. B; AE

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

____ 16.

a. RST WUV ; 5

6c. RST VWU ;

6

5

b. RST UVW ; 5

6 d. The triangles are not similar.

Name: ________________________ ID: A

4

____ 17. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.

a. QRS VTU ; 15

32c. SRQ UTV ;

1

2

b. RSQ TUV ; 1

2d. The triangles are not similar.

____ 18. a. ABCD KLMN ; 9 : 1.8 c. ABCD NKLM ; 9 : 4.68b. ABCD KLMN ; 21.6 : 1.8 d. The polygons are not similar.

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

____ 19.

a. x = 8 c. x = 9

b. x = 11

2d. x = 10

____ 20. a. x = 13 c. x = 5.5b. x = 7 d. x = 10

Name: ________________________ ID: A

5

____ 21. a. 1 c. 4b. 2 d. 20

____ 22. a. 118 b. 29.5 c. 21.7 d. 177

____ 23. 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 design on an piece of paper that is 81

2 in. by 11 in. What are the dimensions of the largest

complete enlargement you can make?

a. 135

in. by 1058

in. c. 81

2in. by 4

38

in.

b. 135

in. by 438

in. d. 81

2in. by 10

58

in.

____ 24. 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. 62

3in. by 10 in. c. 8 in. by 6

2

3in.

b. 51

3in. by 10 in. d. 8 in. by 10 in.

____ 25. In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the diagram, the trees are 4.2 centimeters apart. How far apart should the actual trees be planted?

a. 42 feet c. 42 centimetersb. 420 feet d. 4.2 feet

Name: ________________________ ID: A

6

____ 26. In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 5000 kilometers, what should be the diameter of the drawing of the planet?

a. 10 millimeters c. 100 millimetersb. 2500000 millimeters d. 5000 millimeters

____ 27. Are the two triangles similar? How do you know?

a. yes, by SAS c. yes, by AAb. yes, by SSS d. no

____ 28. Are the triangles similar? How do you know?

a. yes, by SAS b. yes, by SSS c. yes, by AA d. no

____ 29. Are the two triangles similar? How do you know?

a. yes, by SAS b. yes, by SSS c. yes, by AA d. no

Name: ________________________ ID: A

7

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

____ 30.

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

____ 31.

a. ADB CDB; SAS c. ADB CDB; SSSb. ABD CDB; SAS d. The triangles are not similar.

____ 32.

a. OMN OJK; SSS c. OMN JKO; SASb. OMN OJK; SAS d. The triangles are not similar.

Name: ________________________ ID: A

8

____ 33. a. SRQ UTV ; ASA c. RSQ TUV ; ASAb. QRS VTU ; SAS d. The triangles are not similar.

Which theorem or postulate proves the two triangles are similar?

____ 34.

a. SSS Theorem c. AS Postulateb. AA Postulate d. SAS Theorem

____ 35.

a. AA Postulate c. SA Postulateb. SAS Theorem d. SSS Theorem

Name: ________________________ ID: A

9

____ 36. Use the information in the diagram to determine the height of the tree to the nearest foot.

a. 80 ft b. 264 ft c. 60 ft d. 72 ft

____ 37. 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. 20 ft b. 38.4 ft c. 55 ft d. 25 ft

____ 38. 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. 42.3 m b. 47.4 m c. 73.8 m d. 82.8 m

Name: ________________________ ID: A

10

____ 39. The dashed-lined figure is a dilation image of the solid-lined figure. Is the dilation an enlargement, or a reduction? What is the scale factor of the dilation?

a. 6; enlargement c. 3; reduction

b. 3; enlargement d.1

3; reduction

____ 40. The dashed-lined triangle is a dilation image of the solid-lined triangle. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?

a. reduction; 2 b. reduction; 1

4c. enlargement; 2 d. reduction;

1

2

Name: ________________________ ID: A

11

____ 41. The dashed triangle is a dilation image of the solid triangle. What is the scale factor?

a.1

4b.

1

2c.

2

3d. 2

____ 42. A blueprint for a house has a scale of 1 : 35. A wall in the blueprint is 3 in. What is the length of the actual wall?a. 105 feet b. 8.75 feet c. 8.75 in. d. 1,260 feet

____ 43. A microscope shows you an image of an object that is 80 times the object’s actual size. So the scale factor of the enlargement is 80. An insect has a body length of 7 millimeters. What is the body length of the insect under the microscope?a. 56 millimeters c. 5,600 millimetersb. 560 centimeters d. 560 millimeters

____ 44. The zoom feature on a camera lens allows you dilate what appears on the display. When you change from 100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of 5. If the new image is 47.5 millimeters wide, what was the width of the previous image?a. 9.5 millimeters c. 118.75 millimeters b. 23.75 millimeters d. 237.5 millimeters

ID: A

1

Geometry M2 Unit 1 Practice ExamAnswer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 1 Writing a RatioKEY: ratio | word problem DOK: DOK 2

2. ANS: A PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 1 Writing a RatioKEY: ratio | word problem DOK: DOK 2

3. ANS: D PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 1 Writing a RatioKEY: ratio DOK: DOK 2

4. ANS: B PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratio | word problemDOK: DOK 2

5. ANS: D PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratioDOK: DOK 2

6. ANS: B PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 2 Dividing a Quantity into a Given Ratio KEY: ratio | perimeterDOK: DOK 2

7. ANS: C PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 3 Using an Extended Ratio KEY: ratio | extended ratio | word problem DOK: DOK 2

8. ANS: D PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 3 Using an Extended Ratio KEY: ratio | extended ratio | interior angles of a triangle DOK: DOK 2

9. ANS: C PTS: 1 DIF: L3 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a ProportionKEY: proportion | Cross-Product Property DOK: DOK 1

10. ANS: B PTS: 1 DIF: L2 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a ProportionKEY: proportion | Cross-Product Property DOK: DOK 1

11. ANS: A PTS: 1 DIF: L4 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a ProportionKEY: proportion | Cross-Product Property DOK: DOK 2

12. ANS: D PTS: 1 DIF: L4 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 4 Solving a ProportionKEY: proportion | Cross-Product Property DOK: DOK 2

ID: A

2

13. ANS: B PTS: 1 DIF: L2 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Write ratios and solve proportions TOP: 7-1 Problem 5 Writing Equivalent Proportions KEY: proportion | Properties of Proportions | equivalent proportions DOK: DOK 2

14. ANS: D PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 1 Understanding Similarity KEY: similar polygons | corresponding sides DOK: DOK 1

15. ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 1 Understanding Similarity KEY: similar polygonsDOK: DOK 2

16. ANS: B PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 2 Determining Similarity KEY: similar polygons | corresponding sides | corresponding angles DOK: DOK 2

17. ANS: D PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 2 Determining Similarity KEY: similar polygons | corresponding sides | corresponding angles DOK: DOK 2

18. ANS: D PTS: 1 DIF: L4 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 2 Determining Similarity KEY: similar polygonsDOK: DOK 2

19. ANS: C PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportionDOK: DOK 2

20. ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportionDOK: DOK 2

21. ANS: B PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportion | similar polygons DOK: DOK 2

22. ANS: B PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportionDOK: DOK 2

23. ANS: D PTS: 1 DIF: L4 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 4 Using Similarity KEY: similar polygons | word problemDOK: DOK 2

ID: A

3

24. ANS: A PTS: 1 DIF: L4 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 4 Using Similarity KEY: similar polygons | word problemDOK: DOK 2

25. ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 5 Use a Scale Drawing KEY: scale drawing | proportions | word problem DOK: DOK 2

26. ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygons STA: MA.912.G.2.3TOP: 7-2 Problem 5 Use a Scale Drawing KEY: scale drawing | proportions | word problem DOK: DOK 2

27. ANS: C PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 1 Using the AA Postulate KEY: Angle-Angle Similarity PostulateDOK: DOK 2

28. ANS: D PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 1 Using the AA Postulate KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem DOK: DOK 2

29. ANS: C PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 1 Using the AA Postulate KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem DOK: DOK 2

30. ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: Side-Side-Side Similarity TheoremDOK: DOK 2

31. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: Side-Angle-Side Similarity Theorem | corresponding sides DOK: DOK 2

32. ANS: B PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: Side-Side-Side Similarity TheoremDOK: DOK 2

ID: A

4

33. ANS: B PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: corresponding sides | triangle similarity | SAS Theorem DOK: DOK 2

34. ANS: B PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 3 Proving Triangles Similar KEY: Angle-Angle Similarity Postulate | triangle similarity DOK: DOK 2

35. ANS: A PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS Theorems STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 3 Proving Triangles Similar KEY: Angle-Angle Similarity PostulateDOK: DOK 2

36. ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Use similarity to find indirect measurements STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 4 Finding Lengths in Similar Triangles KEY: Angle-Angle Similarity Postulate | word problem DOK: DOK 2

37. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Use similarity to find indirect measurements STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 4 Finding Lengths in Similar Triangles KEY: Angle-Angle Similarity Postulate | word problem DOK: DOK 2

38. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Use similarity to find indirect measurements STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6| MA.912.G.4.8| MA.912.G.5.4| MA.912.G.8.5TOP: 7-3 Problem 4 Finding Lengths in Similar Triangles KEY: Side-Angle-Side Similarity Theorem | word problem DOK: DOK 2

39. ANS: B PTS: 1 DIF: L3 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 1 Finding a Scale Factor KEY: dilation | enlargement | scale factorDOK: DOK 2

40. ANS: D PTS: 1 DIF: L3 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 1 Finding a Scale Factor KEY: dilation | reduction | scale factorDOK: DOK 2

41. ANS: B PTS: 1 DIF: L3 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 1 Finding a Scale Factor KEY: dilation | reduction | scale factorDOK: DOK 2

42. ANS: B PTS: 1 DIF: L3 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 3 Using a Scale Factor to Find a Length KEY: dilation | enlargement | scale factor | word problem DOK: DOK 2

ID: A

5

43. ANS: D PTS: 1 DIF: L3 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 3 Using a Scale Factor to Find a Length KEY: dilation | enlargement | scale factor | word problem DOK: DOK 2

44. ANS: A PTS: 1 DIF: L4 REF: 9-5 DilationsOBJ: 9-5.1 Understand dilation images of figures STA: MA.912.G.2.4| MA.912.G.2.6TOP: 9-5 Problem 3 Using a Scale Factor to Find a Length KEY: dilation | enlargement | scale factor | word problem DOK: DOK 2