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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.
b.
____
b.
c.
d.
3.31 ft
2.60 ft
Their corresponding sides must be proportional and their corresponding areas also
must be proportional.
Their corresponding angles must be the same and their corresponding sides must be
proportional.
Their corresponding angles must be the same and their corresponding areas must be
proportional.
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.
b.
____
c.
d.
2. What is necessary to make the two shapes below similar?
a.
____
4.06 ft
20.21 ft
9000 km
9030 km
c.
d.
9050 km
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.
b.
110
105
c.
d.
1
120
85
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.
b.
19
17
c.
d.
18
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.
a)
4
w
=
18
104
b)
414
128
=
37
x
.
4
Name: ________________________
2. The diagrams
w = 7.8
x = 7.5
y = 3.9
z = 8.4
ID: A
below have the following dimensions:
a = 26
b = 25
c = 13
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:
OBJ:
KEY:
2. ANS:
OBJ:
KEY:
3. ANS:
OBJ:
KEY:
4. ANS:
OBJ:
KEY:
5. ANS:
OBJ:
KEY:
A
PTS:
Geometry
LOC:
Similar Polygons
B
PTS:
Geometry
LOC:
Similar Polygons
A
PTS:
Geometry
LOC:
Scale
A
PTS:
Geometry
LOC:
Scale
A
PTS:
Geometry
LOC:
Similar Triangles
1
G-SO3
DIF: Moderate
REF: 6.1
TOP: Similar Polygons
1
G-SO3
DIF: Difficult
REF: 6.1
TOP: Similar Polygons
1
G-SO3
DIF: Easy
REF: 6.2
TOP: Determining if Two Polygons are Similar
1
G-SO3
DIF: Easy
REF: 6.3
TOP: Drawing Similar Polygons
1
G-SO3
DIF: Moderate
REF: 6.4
TOP: 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:
Width:
1.5 × 12 = 18 ft
1.5 × 10 = 15 ft
The kitchen is 18 ft by 15 ft.
PTS: 1
LOC: G-SO3
DIF: Easy
REF: 6.1
TOP: Similar Polygons
1
OBJ: Geometry
KEY: Similar Polygons
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
LOC: G-SO3
TOP: Similar Polygons
3. ANS:
Side a is equal in length to the side opposite it.
OBJ: Geometry
KEY: Similar Polygons
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
LOC: G-SO3
KEY: Scale
DIF: Easy
REF: 6.2
OBJ: Geometry
TOP: Determining if Two Polygons are Similar
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
LOC: G-SO3
KEY: Scale
6. ANS:
15 × 1.7 = 25.5 m
DIF: Easy
REF: 6.2
OBJ: Geometry
TOP: Determining if Two Polygons are Similar
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
LOC: G-SO3
DIF: Moderate
REF: 6.4
TOP: Similar Triangles
3
OBJ: Geometry
KEY: Similar Triangles
ID: A
9. ANS:
PTS: 1
PROBLEM
1. ANS:
4
w
=
18
104
a)
104 ×
4
w
=
× 104
18
104
104 ×
4
=w
18
23.1 = w
414
128
=
37
x
b)
x × 37 ×
414
128
=
× x × 37
37
x
414x = 128 × 37
x=
128 × 37
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
LOC: G-SO3
DIF: Moderate
REF: 6.4
TOP: Similar Triangles
5
OBJ: Geometry
KEY: Similar Triangles
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.
y
b
=
a
x
y
14.4
=
2.4
1.6
1.6 ×
y
14.4
=
× 1.6
2.4
1.6
1.6 ×
14.4
=y
2.4
9.6 = y
The building is 9.6 m tall.
PTS: 1
LOC: G-SO3
DIF: Difficult
REF: 6.4
TOP: Similar Triangles
6
OBJ: Geometry
KEY: Similar Triangles