Pre-Algebra 8, PRACTICE TEST:
Similarity and Congruence Transformations; Triangle Angle Theorems; Volume
Name: ______________________
Date: ____________Period:_____
1.
What does proportional mean? ______________________________________________________
2.
What does similarity mean? ________________________________________________________
3.
What does the symbol ∼ mean? _____________________________________________________
4.
5.
Jesse bought some new sneakers. He had to borrow money from his big sister. She wants him to pay her
back $7.00 every three weeks. He borrowed $105.00. How long will it take him to pay her back? _____
3
3
It took Bob 1 4 hours to walk 8 of the way home. At the same rate, how many hours would it take Jim to
walk all the way home?
Proportion: _____________________
6.
Solution: _________________
An average person can walk a mile in 15 minutes. At this rate, it takes 18 minutes to walk around the outside
of the Pentagon in Washington, DC. What is the number of feet in the perimeter of the Pentagon?
(5,280 feet = 1 mile)
Proportion: _____________________
Solution: _________________
y
5
7.
The triangles in the picture are similar.
Using the Pythagorean Theorem, find the
���� and �����
distance of 𝐴𝐶
𝐴′𝐶′ (to the nearest tenth).
A’
A
x
B
What is the scale factor for the dilation of
∆ABC → ∆A ' B ' C ' ?
_____________
B’
C’
-5
-5
Pre-Algebra Practice Test: Similarity, Congruence
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8.
���� = 9, 𝑎𝑛𝑑 ����
���� .
∆ 𝐴𝐵𝐶 ~∆ 𝐴𝐷𝐹. (~ means “similar to”) If ����
𝐴𝐵 = 15, 𝐴𝐶
𝐴𝐷 = 5, then find 𝐴𝐹
A
D
B
9.
F
Proportion _________________
C
Name the corresponding sides of ∆𝐴𝐵𝐶 to ∆𝑈𝑉𝑊.
U
C
B
10.
Solution__________
A
W
V
���� ∼_________
𝐴𝐵
����
𝐶𝐴 ∼_________
���� ∼________
𝐵𝐶
Find the volume of the ice cream in the cone. Leave your answer in terms of π.
10. __________________
11.
In Geoville each avenue is perpendicular to each street. A partial map of Geoville is shown. The measure of
∠VYS , formed by Pythagoras St. and Diagonal Blvd., is 35° .
Find the m∠WXU _______________
List two triangles similar to ∆YSV
____________ and _______________
Pre-Algebra Practice Test: Similarity, Congruence
Revised 2014 - CCSS
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12.
In ∆ABC , m∠A = 3 x + 40 , m∠B = 3 x + 20 , and m∠C = 6 x − 36 .
What is the measure of m∠B ?
Picture/Work
m∠B _________________
13.
(SE) The two triangles in the picture are similar. What is the value of x?
(A) x = 3b
14.
(B)
x=
b
3b
(C)
x=
a
3b
(D) x =
3b
a
1
(SE) Triangle ABC is similar to triangle KLM where the ratio of proportionality is 6 , and AB = 24 centimeters.
B
What is KL?
L
(A) 4 cm
(C) 8 cm
(B) 48 cm
(D) 144 cm
K
A
15.
16.
M
C
(SE) Which sequence of transformations creates congruent figures? Circle all that apply.
(A) Reflect then dilate
(C) Dilate then rotate
(B) Rotate then translate
(D) Translate then dilate
(SE) The vertices of ∆𝐴𝐵𝐶 have coordinates of 𝐴(0, 0), 𝐵(0, 4), and 𝐶(6, 0). A second triangle, which is a
transformation of the first, has the same vertex 𝐴. If its other vertices are 𝐵’(2, 0) and 𝐶’(0, −3),
Draw and label the triangles, read the statements, then
answer the question below.
I.
II.
III.
IV.
One triangle is a dilation of the other.
One triangle is a rotation of the other.
One triangle is congruent to the other.
One triangle is similar to the other.
Which of the following statements are true?
A. I only
B. II only
C. IV only
D. I, II and IV
E. I and IV
Pre-Algebra Practice Test: Similarity, Congruence
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17.
18.
19.
(SE) Which transformation(s) maintain congruence? Circle all that apply.
(A) Reflection
(C) Rotation
(B) Dilation
(D) Translation
(SE) Given that ∆ABC is congruent to ∆DFE , find the measure of ∠D .
(A) 30°
(C) 40°
(B) 60°
(D) 140°
(SE) ∆PQR is congruent to ∆TUV . Which statement is not true?
(A) PQ = 5
(B) VT = 4
6
(C) The area of ∆TUV =
(D) TV = 3
20.
21.
(SE) Triangles ABC and DEF are similar. What is the measure of angle F?
(A) 35°
(C) 65°
(B) 55°
(D) 180°
(SE) The four triangles below are not drawn to scale.
Based on the given information, which of the triangles would be similar to each other?
22.
(A) I and II
(C) I and III
(B) II and IV
(D) I, III and IV
1
(SE) ∆ABC  ∆DEF , AC = 5 . DF = 2 , BC = 3 .
2
What is the length of EF ?
(A) 1
(B) 2
Pre-Algebra Practice Test: Similarity, Congruence
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2
(C) 1
1
2
Picture/Work
(D) 3
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