Math 8 Unit 4 PRACTICE TEST Part 1
BUTTERFLIES, PINWHEELS, AND WALLPAPER
Name: _______________________________________
Date:______________________ Hour:___________
2014-2015
Problem
Numbers
Butterflies, Pinwheels, and Wallpaper
I can identify transformations as reflections, rotations,
and translations.
I can reflect a shape in a line, rotate a shape about a
point, and translate a shape given specific distance and
direction.
I can use transformations to prove that two triangles
are congruent.
I can determine whether or not two triangles are
congruent using information about their parts.
I can use coordinate (motion) rules for basic rigid
transformations.
I can find the measures of angles formed by parallel
lines cut by a transversal.
I can dilate a figure on a coordinate plane when given
the center and a scale factor.
I can identify similar figures using transformations or
measures of corresponding parts.
I can use the properties of congruent or similar
triangles to solve problems of indirect measurement.
Transformation A
Transformation B
B’
B
Points
Possible
1-4
4
5-7
6
8-9
4
10-13
4
14-16
4
17-20
4
21-22
4
23-26
4
27-28
6
Transformation C
B
C’
C
C’
B’
B
C
C’
B’
A’
Choose the transformation above that matches each of the following descriptions.
1. A 180° rotation around point 𝐶
_____________
2. A reflection
_____________
3. A translation up and to the right
_____________
4. A 90° counterclockwise rotation around point 𝐵 _____________
5. Reflect the figure in line 𝑙. Label the image.
𝑙
D
Scale
Score
Transformation D
B
C
(2 points)
A
A’
A
C
A
Percent
Correct
A
A’
A
Points
Earned
C’
A’
B’B
C
6. Rotate quadrilateral 𝑃𝑄𝑅𝑆 90° counterclockwise about point 𝑅. Label the image. (2 points)
P
Q
R
S
A
7. Translate the shape so that
point 𝐵 moves to point 𝐵′.
Label the image.
(2 points)
B
𝐵′
D
C
8. __________ Which set of transformations proves that 𝐴𝐵𝐶𝐷 ≅ 𝐴′𝐵′𝐶′𝐷′? (2 points)
A. Reflect 𝐴𝐵𝐶𝐷 in ̅̅̅̅
𝐵𝐷. Translate 𝐴𝐵𝐶𝐷 so that point B moves onto point B’.
B. Translate 𝐴𝐵𝐶𝐷 so that point B moves onto point B’. Rotate
90° counterclockwise about point B.
C. Rotate 180° about point D. Translate so that point B moves
B’
D’
A’
C’
onto point B’
9. __________ Which set of transformations would prove that ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐵𝐷? (2 points)
A. Translate ∆𝐴𝐵𝐶 so that point C moves onto point B
Reflect ∆𝐴𝐵𝐶 in line 𝑚.
B. Rotate ∆𝐴𝐵𝐶 180° counterclockwise about point C.
Translate ∆𝐴𝐵𝐶 so that point C moves onto point D.
C. Rotate ∆𝐴𝐵𝐶 90° counterclockwise about point B.
Look at each pair of triangles and then choose the statement that best describes them.
10. __________
11. __________
A.
B.
C.
D.
Congruent due to the SAS rule.
Congruent due to the ASA rule.
Congruent due to the AAS rule.
There is not enough information provided to prove that
these triangles are congruent.
A.
B.
C.
D.
Congruent due to the SSS rule.
Congruent due to the SSA rule.
Congruent due to the SAS rule.
There is not enough information provided to prove that
these triangles are congruent.
12. __________
A.
B.
C.
D.
Congruent due to the SSS rule.
Congruent due to the AAS rule.
Congruent due to the SAS rule.
There is not enough information provided to prove that
these triangles are congruent.
13. __________
A.
B.
C.
D.
Congruent due to the SSS rule.
Congruent due to the SSA rule.
Congruent due to the SAS rule.
There is not enough information provided to prove that
these triangles are congruent.
14. __________ Which of the following coordinate rules represents a reflection in the 𝑦-axis?
A. (𝑥, 𝑦) → (−𝑥, −𝑦)
B. (𝑥, 𝑦) → (4𝑥, 4𝑦)
C. (𝑥, 𝑦) → (−𝑥, 𝑦)
D. (𝑥, 𝑦) → (𝑦, 𝑥)
15. Which rule describes the translation of 𝐽𝐾𝐿𝑀 to 𝐽’𝐾’𝐿’𝑀’?
A. (𝑥, 𝑦) → (𝑥 − 6, 𝑦 + 2)
B. (𝑥, 𝑦) → (𝑥 − 2, 𝑦 + 6)
C. (𝑥, 𝑦) → (𝑥 − 6, 𝑦 − 2)
D. (𝑥, 𝑦) → (𝑥 + 6, 𝑦 − 2)
16. 𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝐴𝐵𝐶𝐷 is drawn below.: A(−3, 3), B (2, 3), C (4, 1), and D (−1, 1). Complete the
table according to the coordinate rule (𝑥, 𝑦) → (𝑥, −𝑦).
Then draw and label the image. (2 points)
A
B
D
C
Point
Original
Coordinates
Coordinates
after
(𝑥, 𝑦) → (𝑥, −𝑦)
A
(−3, 3)
𝐿𝑖𝑛𝑒 𝑙 and 𝑙𝑖𝑛𝑒 𝑚 are parallel. Find the measures of the angles.
17. ∠ 𝑑 ____________
18. ∠ 𝑒 ____________
19. ∠ 𝑖 ____________
20. ∠𝑝 ____________
B
(2, 3)
C
(4, 1)
D
(−1, 1)
Math 8 Unit 4 PRACTICE TEST Part 2
BUTTERFLIES, PINWHEELS, AND WALLPAPER
21. Dilate quadrilateral ABCD with a scale
factor of 4. Label the image. (2 points)
Name: _______________________________________
Date:______________________ Hour:___________
22. Dilate triangle XYZ according to the rule
1
1
(𝑥 𝑦) → ( 𝑥, 𝑦). Label the image.
3
3
(2 points)
A
A
B
D
C
C
B
1
23. ___________ Triangle 𝑋𝑌𝑍 is dilated with a scale factor of 2. Which statement is NOT true about the
image 𝑋’𝑌’𝑍’?
A.
B.
C.
D.
1
The sides will be 2 as long.
The sides will have the same slope.
The angles will be the same.
1
The area will be 2 of the area.
24. What information would you need to prove that ∆𝐴𝐵𝐶 is similar to ∆𝐷𝐸𝐹 using the AA property?
P
25. __________ Which set of transformations would prove
that ∆𝑅𝑆𝑇 is similar to ∆𝑃𝑄𝑇 ?
9 cm
R
3 cm
Q
S 6 cm
A. Translate ∆𝑅𝑆𝑇 so that point R moves onto point P. Dilate ∆𝑅𝑆𝑇 according to the motion rule
(𝑥, 𝑦) → (3𝑥, 3𝑦).
B. Translate ∆𝑅𝑆𝑇 so that point 𝑆 moves onto point 𝑄. Dilate ∆𝑅𝑆𝑇 with a scale factor of 2.
1
C. Translate ∆𝑃𝑄𝑇 so that point Q moves onto point S. Dilate ∆𝑃𝑄𝑇 with a scale factor of .
2
T
T
26. __________ Which set of triangles below could be proven similar by AA property?
B.
A.
D.
C.
27. Don and Adam use the mirror method to estimate the height of a tall building.
a) Label the following measurements on the picture below. (1 point)

Height from the ground to Don’s eyes: 2 meters

Distance from the middle of the mirror to Don’s feet: 1.5 meters

Distance from the middle of the mirror to the bottom of the building: 9 meters
b) Use the properties of similarity to find the height of the building. Show your work.
(2 points)
The height of the building is ______________ meters.
28. A tall tree casts a 24-foot shadow at the same time that a 4-foot wall casts a 6-foot shadow. How
tall is the tree?
a) Label the picture below with these measurements. (1 point)
b) Use the properties of similarity to find the height of the tree. Show your work. (2 points)
The height of the tree is ______________ feet.