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

Ch. 6 Practice Test

Multiple Choice

Identify the choice that best completes the statement or answers the question

____ 1. A doorway of width 3.25 ft and height 7.25 ft is similar to another doorway of width x and height 9.06

ft. What is the measure of x?

a. 4.06 ft c. 3.31 ft

b. 20.21 ft d. 2.60 ft

____ 2. What is necessary to make the two shapes below similar?

a. Their corresponding sides must be proportional and their corresponding areas also

must be proportional

b. Their corresponding angles must be the same and their corresponding sides must be

proportional

c. Their corresponding angles must be the same and their corresponding areas must be

proportional

d. Their corresponding angles must be supplementary and their corresponding sides must

be proportional

____ 3. If the scale on a map of the world is 750 km:1 cm, what distance would be represented by 12 cm on the

map?

a. 9000 km c. 9050 km

b. 9030 km d. 8970 km

____ 4. A drawing of a staircase measures 6 cm in height, but the actual staircase measures 660 cm in height

What is the scale factor?

a. 110 c. 120

b. 105 d. 85

1

Name: ________________________ ID: A

____ 5. A right triangle has a base of 46 cm. A similar triangle has a base of 874 cm. How many times larger is

the similar triangle?

a. 19 c. 18

b. 17 d. 20

Short Answer

1. On the blueprint for a kitchen floor, the room measures 12 inches long and 10 inches wide. If the scale

of the drawing is 1 inch:1.5 ft, what are the dimensions of the actual kitchen floor?

2. Are the triangles below similar? Explain

3. In the diagram below, 1 cm:9.3 m. What is the length of side a in metres? (The figure is not drawn to

scale.)

2

Name: ________________________ ID: A

4. Janine constructed a dollhouse modelled after her own house. The hallway of the dollhouse is 6 inches

long and 4 inches wide. If the hallway in her actual house is 9 feet long and 5 feet wide, is the dollhouse

actually similar to Janine’s house?

5. The diagrams below have the following dimensions:

w = 22.1 mm a = 3.3 mm

x = 10.725 mm b = 6.1 mm

y = 19.825 mm c = 3 mm

z = 9.75 mm d = 6.8 mm

Are the two objects similar shapes? Explain

6. What would be the length of a if the diagram below were scaled by a factor of 1.7?

7. A triangle has two interior angles of 37° and 82°. A second triangle has two interior angles of 37° and

61°. Are these two triangles similar? Explain

8. A triangle has side lengths of 32.7 mm, 47.7 mm, and 65.4 mm. The longest side of a similar triangle is

719.4 mm. What are the lengths of its other two sides?

3

Name: ________________________ ID: A

9. Gina drew a scale representation of a field (see Polygon C). For instance, she drew a line

2.2 cm to represent the actual measure (20 m) of this side (AD). Gina needs to complete the drawing

of Polygon D so that both polygons are similar

Problem

1. Determine the value of the variable, rounded to 1 decimal place

4 w

a) =

18 104

414 128

b) =

37 x

4

Name: ________________________ ID: A

2. The diagrams below have the following dimensions:

w = 7.8 a = 26

x = 7.5 b = 25

y = 3.9 c = 13

z = 8.4 d = 28

If the smaller figure was created as a reduction of the larger figure, what scale factor was used?

3. Calculate the value of side length x in the diagram if:

a = 6 cm

b = 9 cm

c = 8 cm

4. In the picture below, a man observes his shadow on the ground. The casting of his shadow creates a

similar triangle to that of the nearby building. If a is 2.4 m and b is 14.4 m, how tall is the building if the

man is 1.6 m tall?

5

ID: A

Ch. 6 Practice Test

Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: Moderate REF: 6.1

OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons

KEY: Similar Polygons

2. ANS: B PTS: 1 DIF: Difficult REF: 6.1

OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons

KEY: Similar Polygons

3. ANS: A PTS: 1 DIF: Easy REF: 6.2

OBJ: Geometry LOC: G-SO3 TOP: Determining if Two Polygons are Similar

KEY: Scale

4. ANS: A PTS: 1 DIF: Easy REF: 6.3

OBJ: Geometry LOC: G-SO3 TOP: Drawing Similar Polygons

KEY: Scale

5. ANS: A PTS: 1 DIF: Moderate REF: 6.4

OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles

KEY: Similar Triangles

SHORT ANSWER

1. ANS:

The scale of the blueprint is 1 inch:1.5 ft. To calculate the dimensions of the room, multiply each

measurement on the blueprint by 1.5 and change the units from inches to feet

Length: 1.5 × 12 = 18 ft

Width: 1.5 × 10 = 15 ft

The kitchen is 18 ft by 15 ft

PTS: 1 DIF: Easy REF: 6.1 OBJ: Geometry

LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons

1

ID: A

2. ANS:

No, the triangles are not similar. This can be determined by comparing the corresponding angles of the

two triangles

Both triangles are right triangles, but their other two angles are not corresponding

Calculate the other angle of the bottom triangle

180° – 90° – 38.1° = 51.9°

38.1° ≠ 36.7°

51.9° ≠ 53.3°

None of the angles of the bottom triangle are equal to the angles of the top triangle; therefore, the

triangles are not similar

PTS: 1 DIF: Moderate REF: 6.1 OBJ: Geometry

LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons

3. ANS:

Side a is equal in length to the side opposite it

1 cm equals 9.3 m, so multiply the length of the opposite side on the diagram by 9.3

9.4 cm × 9.3 m/cm ≈ 87.4 m

The length of d is 87.4 m

PTS: 1 DIF: Difficult REF: 6.1 OBJ: Geometry

LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons

4. ANS:

For the dollhouse and house to be similar, their dimensions must be proportional

Length: 9 ÷ 6 = 1.5

Width: 5 ÷ 4 = 1.25

1.5 ≠ 1.25

The scale factors of the dimensions of the hallway are not the same, so the dollhouse is not similar to

the actual house

PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry

LOC: G-SO3 TOP: Determining if Two Polygons are Similar

KEY: Scale

2

ID: A

5. ANS:

Match up the corresponding sides by rotating the second object by 180°. Calculate whether the ratios

between the side lengths of the two shapes are equal

w ÷ d = 22.1 ÷ 6.8

w ÷ d = 3.25

x ÷ a = 10.725 ÷ 3.3

x ÷ a = 3.25

y ÷ b = 19.825 ÷ 6.1

y ÷ b = 3.25

z ÷ c = 9.75 ÷ 3

z ÷ c = 3.25

The ratios are the same, so the shapes are similar

PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry

LOC: G-SO3 TOP: Determining if Two Polygons are Similar

KEY: Scale

6. ANS:

15 × 1.7 = 25.5 m

The length of a would be 25.5 m

PTS: 1 DIF: Easy REF: 6.3 OBJ: Geometry

LOC: G-SO3 TOP: Drawing Similar Polygons KEY: Scale

7. ANS:

Yes. The first triangle has interior angles of 37°, 82°, and 61°, because the sum of the angles in any

triangle is 180°. The second triangle has the same interior angles using the same rule

PTS: 1 DIF: Easy REF: 6.4 OBJ: Geometry

LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles

8. ANS:

Calculate the scale factor between the longest sides of the two triangles

719.4 ÷ 65.4 = 11

The larger triangle is 11 times bigger than the smaller triangle. Calculate the lengths of the other two

sides

32.7 × 11 = 359.7 mm

47.7 × 11 = 524.7 mm

The other two sides of the larger triangle are 359.7 mm and 524.7 mm

PTS: 1 DIF: Moderate REF: 6.4 OBJ: Geometry

LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles

3

ID: A

9. ANS:

PTS: 1

PROBLEM

1. ANS:

4 w

a) =

18 104

4 w

104 × = × 104

18 104

4

104 × =w

18

23.1 = w

414 128

b) =

37 x

414 128

x × 37 × = × x × 37

37 x

414x = 128 × 37

128 × 37

x=

414

x = 11.4

PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry

LOC: G-SO3 TOP: Determining if Two Polygons are Similar

KEY: Proportional reasoning

4

ID: A

2. ANS:

Calculate the ratio between the side lengths

7.8 ÷ 26 = 0.3

7.5 ÷ 25 = 0.3

3.9 ÷ 13 = 0.3

8.4 ÷ 28 = 0.3

Each set of corresponding sides are related by a factor of 0.3. The scale factor is 0.3

PTS: 1 DIF: Easy REF: 6.3 OBJ: Geometry

LOC: G-SO3 TOP: Drawing Similar Polygons KEY: Scale

3. ANS:

ΔABC and ΔADE are similar because they share ∠A, and right triangles are similar if one pair of

corresponding angles is congruent

Calculate the ratio of side lengths

b 9

=

a 6

b

= 1.5

a

Therefore, the ratio between AB and AD must be 1.5

AD

= 1.5

AB

c+x

= 1.5

c

c + x = c × 1.5

x = (c × 1.5) − c

x = (8 × 1.5) − 8

x = 12 − 8

x = 4 cm

Side length x is 4 cm long

PTS: 1 DIF: Moderate REF: 6.4 OBJ: Geometry

LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles

5

ID: A

4. ANS:

Since the triangles are similar, a must be proportional to b, and x and y must be in the same proportion

b y

=

a x

14.4 y

=

2.4 1.6

14.4 y

1.6 × = × 1.6

2.4 1.6

14.4

1.6 × =y

2.4

9.6 = y

The building is 9.6 m tall

PTS: 1 DIF: Difficult REF: 6.4 OBJ: Geometry

LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles

6

719.4 ÷ 65.4 = 11 The larger triangle is 11 times bigger than the smaller triangle. Calculate the lengths of the other two sides. 32.7 ×11 = 359.7 mm 47.7 ×11 = 524.7 mm The other two sides …