Practice Test Chapter 6. The test for chapter 6 is LONG if your algebra skills or chapter 6
knowledge is weak. Practice by taking this practice test in a timed situation.
Short Answer
1. 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?
1
1
2. The length of a rectangle is 6 inches and the width is 4 inches. What is the ratio, using whole numbers, of
2
4
the length to the width?
3. A salsa recipe uses green pepper, onion, and tomato in the extended ratio 1 : 3 : 9. How many cups of onion
are needed to make 117 cups of salsa?
4. solve
5. Given the proportion
, what ratio completes the equivalent proportion
?
6. Are the polygons similar? If they are, write a similarity statement and give the scale factor. ALso state
the shortcut that allows you to state the polygons are similar.
S
V
10
12
T
15
32º
W
R
32º
U
18
Not drawn to scale.
7. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.
Are the polygons similar? If they are, write a similarity statement and give the scale factor. ALso state
the shortcut that allows you to state the polygons are similar.
8. Are the polygons similar? If they are, write a similarity statement and give the scale factor. Why?
A
21.6
B
N
1.8
K
9
9
4.68
4.68
D
C
21.6
M
1.8
L
Not drawn to scale.
What similarity statement can you write relating the three triangles in the diagram?
U
V
T
9.
W
Determine which pair of polygons is similar. Justify your answer.
10.
11. Are the two triangles similar? If so, Write a similarity statement. Aso state the shortcut that allows you to
state the polygons are similar.
J
H
M
39 °
39 º
K
G
Which theorem or postulate proves the two triangles are similar?
12.
4
8
>
2
>
Not drawn to scale.
13. Use the information in the diagram to determine the height of the tree to the nearest foot.
14. 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.
15. What is the value of x?
x–2
x
>
x+5
x+1
>
16. For what value of x so that
?
A
x
B
11
E 5 D
7
C
17. What is the value of x? What theorem allows you to find this?
>
3x
4x
3x + 7
>
>
5x – 8
18. Plots of land between two roads are laid out according to the boundaries shown. The boundaries between the
two roads are parallel. What is the length of Plot 3 along Cheshire Road?
Sh elb y
R
48
PLOT 3
PLOT 4
>
PLOT 2
>
>
PLOT 1
Cheshire Road
>
>
40
yards
o ad
yards
56
yards
19. Of the 112 students in the marching band, 35 were in the drum section. What is the ratio of drummers to other
musicians in the band?
20. When a 9-foot tall garden shed cast a 5-foot 3-inch shadow, a house cast a 28-foot shadow. Find the height of
the house.
21.
ABC
FGH, AB = 24, AC = 16, GH = 9, and FH = 12. Find the scale factor of
ABC to
FGH.
22. Is the dilation a similarity transformation? Verify your answer.
23. If
FGH
LMN and
and
are medians, find BL.
24. The ratio of the measures of the three angles of a triangle is 3:4:8. Find the measure of the largest
angle.
25. In
PQR,
bisects
PQR. Find the value of x. What theorem allows you to complete this problem?
26. Find the value of x so that
27. If
FGH
.
JKL, find GX. What theorem allows you to find this value?
28. Find the value of y.
29. Find SR.
30. Lacy made a scale model of her house. Her house is 54 feet tall. Her model is 6 inches tall. What is the scale
of the model? (Simplify) How many times as tall as her house is her model?
31. Know all of the definitions, theorems, postulates for this chapter and when to use them.
Know how to prove two triangles similar using shortcuts. Know which shortcuts are needed and which are
redundant. Read the key concepts carefully.
32. In Triangle ABC, AB = 10, BC = 16, and DE = 6. Write a similarity statement that shows that the two triangles
are similar then Find CD.
Use the figure below to answer the following questions.
33. Identify the similar triangles. Then solve for x.
34.
35.
36. The sides of a quadrilateral are 15’, 9’, 18’, and 12’. The longest side of a similar quadrilateral is
40’. What is the ratio of the shortest side of the similar quadrilateral to the perimeter of the similar
quadrilateral?
Practice Test Chapter 7. The test for chapter 7 is LONG if your algebra skills or chapter 7
knowledge are weak. Practice taking this practice test in a timed situation.
Answer Section
SHORT ANSWER
1. ANS:
1 : 725
PTS: 1
DIF: L3
REF: 7-1 Ratios and Proportions
OBJ: 7-1.1 Write ratios and solve proportions
TOP: 7-1 Problem 1 Writing a Ratio
KEY: ratio | word problem
DOK: DOK 2
2. ANS:
26 : 17
PTS: 1
DIF: L3
REF: 7-1 Ratios and Proportions
OBJ: 7-1.1 Write ratios and solve proportions
TOP: 7-1 Problem 1 Writing a Ratio
KEY: ratio
DOK: DOK 2
3. ANS:
27
PTS:
OBJ:
TOP:
KEY:
4. ANS:
1
DIF: L3
REF: 7-1 Ratios and Proportions
7-1.1 Write ratios and solve proportions
7-1 Problem 3 Using an Extended Ratio
ratio | extended ratio | word problem
DOK: DOK 2
PTS: 1
DIF: L4
REF: 7-1 Ratios and Proportions
OBJ: 7-1.1 Write ratios and solve proportions
TOP: 7-1 Problem 4 Solving a Proportion
KEY: proportion | Cross-Product Property
DOK: DOK 2
5. ANS:
PTS:
OBJ:
TOP:
KEY:
DOK:
6. ANS:
1
DIF: L2
REF: 7-1 Ratios and Proportions
7-1.1 Write ratios and solve proportions
7-1 Problem 5 Writing Equivalent Proportions
proportion | Properties of Proportions | equivalent proportions
DOK 2
;
PTS: 1
DIF: L3
REF: 7-2 Similar Polygons
OBJ: 7-2.1 Identify and apply similar polygons
STA: MA.912.G.2.3
TOP: 7-2 Problem 2 Determining Similarity
KEY: similar polygons | corresponding sides | corresponding angles
DOK: DOK 2
7. ANS:
The triangles are not similar.
PTS: 1
DIF: L3
REF: 7-2 Similar Polygons
OBJ: 7-2.1 Identify and apply similar polygons
STA: MA.912.G.2.3
TOP: 7-2 Problem 2 Determining Similarity
KEY: similar polygons | corresponding sides | corresponding angles
DOK: DOK 2
8. ANS:
The polygons are not similar.
PTS:
OBJ:
TOP:
DOK:
9. ANS:
PTS:
OBJ:
STA:
TOP:
DOK:
10. ANS:
1
DIF: L4
REF: 7-2 Similar Polygons
7-2.1 Identify and apply similar polygons
STA: MA.912.G.2.3
7-2 Problem 2 Determining Similarity
KEY: similar polygons
DOK 2
1
DIF: L3
REF: 7-4 Similarity in Right Triangles
7-4.1 Find and use relationships in similar triangles
MA.912.G.2.3| MA.912.G.4.6| MA.912.G.5.2| MA.912.G.5.4| MA.912.G.8.3
7-4 Problem 1 Identifying Similar Triangles
KEY: similar triangles | altitude
DOK 2
I is similar; the angles are congruent and
=
.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
PTS: 1
DIF: Average
OBJ: 9-2.1 Identify similar polygons.
NAT: NCTM GM.1b | NCTM GM.1
STA: FL MA.B.1.4.3 | FL MA.C.2.4.1 | FL MA.C.3.4.1 | FL MA.A.3.4.3
TOP: Identify similar polygons.
KEY: similar | polygon
11. ANS:
yes, by AA
PTS: 1
DIF: L2
REF: 7-3 Proving Triangles Similar
OBJ: 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.8.5
TOP: 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
12. ANS:
AA Postulate
PTS:
OBJ:
STA:
TOP:
KEY:
13. ANS:
80 ft
1
DIF: L3
REF: 7-3 Proving Triangles Similar
7-3.1 Use the AA Postulate and the SAS and SSS Theorems
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.8.5
7-3 Problem 3 Proving Triangles Similar
Angle-Angle Similarity Postulate | triangle similarity
DOK: DOK 2
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: L3
REF: 7-3 Proving Triangles Similar
7-3.2 Use similarity to find indirect measurements
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.8.5
7-3 Problem 4 Finding Lengths in Similar Triangles
Angle-Angle Similarity Postulate | word problem
DOK: DOK 2
14. ANS:
20 ft
PTS:
OBJ:
STA:
TOP:
KEY:
15. ANS:
5
1
DIF: L4
REF: 7-3 Proving Triangles Similar
7-3.2 Use similarity to find indirect measurements
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.8.5
7-3 Problem 4 Finding Lengths in Similar Triangles
Angle-Angle Similarity Postulate | word problem
DOK: DOK 2
PTS:
OBJ:
STA:
TOP:
DOK:
16. ANS:
1
DIF: L4
REF: 7-5 Proportions in Triangles
7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem
MA.912.G.2.3| MA.912.G.4.5| MA.912.G.4.6
7-5 Problem 1 Using the Side-Splitter Theorem
KEY: Side-Splitter Theorem
DOK 2
PTS:
OBJ:
STA:
TOP:
DOK:
17. ANS:
1
DIF: L4
REF: 7-5 Proportions in Triangles
7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem
MA.912.G.2.3| MA.912.G.4.5| MA.912.G.4.6
7-5 Problem 1 Using the Side-Splitter Theorem
KEY: Side-Splitter Theorem
DOK 2
52/3 and the theorem is the side splitter theorem
PTS: 1
DIF: L4
REF: 7-5 Proportions in Triangles
OBJ: 7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem
STA: MA.912.G.2.3| MA.912.G.4.5| MA.912.G.4.6
TOP: 7-5 Problem 2 Finding a Length
KEY: corollary of Side-Splitter Theorem DOK: DOK 2
18. ANS:
2
46 yards
3
PTS:
OBJ:
STA:
KEY:
19. ANS:
5:11
1
DIF: L3
REF: 7-5 Proportions in Triangles
7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector Theorem
MA.912.G.2.3| MA.912.G.4.5| MA.912.G.4.6
TOP: 7-5 Problem 2 Finding a Length
corollary of Side-Splitter Theorem | word problem
DOK: DOK 2
PTS: 1
20. ANS:
48 ft
PTS: 1
21. ANS:
PTS: 1
22. ANS:
No. The legs of the right triangles are not proportional.
PTS: 1
23. ANS:
2.2
PTS: 1
24. ANS:
96
PTS: 1
25. ANS:
9.5, Triangle angle bisector theorem
PTS: 1
26. ANS:
2
PTS: 1
27. ANS:
5
PTS: 1
28. ANS:
28
PTS: 1
29. ANS:
11
PTS: 1
30. ANS:
see
PTS: 1
31. ANS:
s
PTS: 1
32. ANS:
48/5
PTS: 1
33. ANS:
PQR
PTS: 1
34. ANS:
STR
PTS: 1
35. ANS:
36. ANS:
1/6