Download Grade 8 Geometry Review 1.(8G1a) Which sequence of

Grade 8 Geometry Review
1.(8G1a)
Which sequence of transformations takes
A
B
C
D
A to its image,
B ?
reflection over the x-axis and translation 2 units down
reflection over the y-axis and translation 2 units down
translation 2 units down and 900 rotation a b o u t the origin
translation 12 units right and 900 rotation a b o u t the origin
2. (8G5)
In the diagram below, rays g and h are parallel. Triangle JKL has vertices J and L on ray g
and vertex K on ray h. The sum of the measures of
1 and 2 is 1520
What is the measure, in degrees, of
A 28
B 38
3?
C 62
D 208
3. (8G4)
Rectangle R undergoes a dilation with scale factor 0.5 and then a reflection over the y-axis.
The resulting image is Rectangle S . Which statement about Rectangles R and S is true?
A They are congruent and similar.
C They are congruent but not similar.
B They are similar but not congruent.
D They are neither congruent nor similar.
4. (8G3)
Vertex J of rectangle FGHJ is located at (4, 2). A dilation of FGHJ will result in the image
F'G'H'J'. If the dilation is centered at the origin and has a scale factor of 2, what are the
coordinates of J'?
A (8,4)
B (7,6)
C (4,2)
D (2,1)
5. (8G1a)
Giselle will transform ∆XYZ shown below, using only rotations, reflections, and translations.
The vertices of ∆XYZ have integer coordinates. What is the length of the image of XY after Giselle
transforms the figure?
A any length less than 4 units
C any length greater than 4 units
B exactly 4 units
D any length
6. (8G4)
The image of ∆ABC after two transformations is ∆A’B’C’, as shown on the coordinate grid below.
Which sequence best describes these two transformations?
A dilation and then translation
B dilation and then reflection
C reflection and then rotation
D translation and then rotation
7.(8G5)
In the figure below, lines a and b are parallel and line c is a transversal.
Which statement explains why
A
B
C
D
2 is congruent to
6
The angles form a straight line.
The angles are on opposite sides of the transversal.
The angles have measures that sum to a straight angle.
The angles have the same relative positions on the transversal.
8.(7G5)
In the diagram of ∆RST below,
S measures 54° and
form an exterior angle of 115°,
T measures x0. Side SR is extended to
What is the value of x, in degrees?
A 36
B 61
C 115
9. (8G3)
The rectangle shown below is to be reflected over the y-axis.
Which statement about the resulting image will be true?
A
B
C
D
All
All
All
All
x coordinates and y coordinates are positive.
x coordinates and y coordinates are negative.
x coordinates are positive and all y coordinates are negative.
x coordinates are negative and all y coordinates are positive.
D 126
1 0 .(8G9)
A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of
32π cubic feet. What is the diameter, in feet, of the water tank?
A 16
B 10
C 8
D 4
11.(8G3)
If ∆ABC is rotated 900 clockwise about the origin, what will be the new coordinates of vertex B?
I
A (-1, -4)
B (1, 4)
C (4, 1)
D (4, -1)
12.(8G9)
A spherical ball has a radius of 4 inches. What is the volume, in cubic inches, of the ball in terms
of π?
A 64π
3
B 48π
C 64π
D 256π
3
13.(8G1b)
Quadrilateral PQRS will be rotated 200 clockwise about point Q.
What is the measure of
A 200
PQR as a result of this rotation?
B 570
C 770
D 970
14.(8G2)
Triangle ABC was rotated 900 clockwise. Then it underwent a dilation centered at the origin with a
scale factor of 4. Triangle A'B'C' is the resulting image.
What parts of ∆A'B'C' are congruent to the corresponding parts of the original triangle? Explain
your reasoning.
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Compare the perimeters of ∆ABC and ∆A'B'C'. Explain your reasoning.
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15. (8G3)
Pentagon D, on the coordinate plane below, is the image of pentagon C after a sequence of
transformations.
Describe a sequence of transformations that will take pentagon C to its image, pentagon D
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16. (8G9)
Mr. Tarpey wanted his students to compare the volumes of a sphere with a diameter of
6 centimeters (cm) and a cylinder with a diameter of 6 cm and height of 6 cm. Determine
the volume of each figure to the nearest cubic centimeter. Which solid figure has the
greater volume?
Volume of sphere =
4
πr3
3
Show your work.
Sphere ___________ cm3
Cylinder___________cm3
___________________ has a greater volume