Download Grade 8 Unit 3 Common Assessment - Joliet Public Schools District 86

Grade 8 Unit 3
Common Assessment
Name____________________________
Date_____________
8. G.2/8.G.4
1. Rectangle P is dilated about the origin with a scale factor of 0.5 and then reflected over the y-axis.
The new image is Rectangle T. Which statements are true about Rectangle P and Rectangle T?
A. They are congruent but not similar because dilation with a scale factor other than 1 changes
the lengths of the sides but not the shape of the figure.
☐ TRUE
☐ FALSE
B. They are similar but not congruent because dilation with a scale factor other than 1 changes
the lengths of the sides but not the shape of the figure.
☐ TRUE
☐ FALSE
C. They are congruent and similar because the rigid motion did not change the size or shape of
the figure.
☐ TRUE
☐ FALSE
D. They are neither congruent nor similar because the rigid motion changed the size and the
shape of the figure.
☐ TRUE
☐ FALSE
8.G.5/8.EE.7
2.
A. Find the measure of angle A.
☐ 9°
☐ 63°
☐ 77°
☐ 117°
Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3
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B. Justify the steps you took to solve Part A.
8. G. 5
3. Read the problem and evaluate Melinda’s method for finding the missing angle. Explain why
Melinda’s answer is incorrect and correct her error.
?
150°
85°
I solved the problem by first subtracting
150° from 180° to find the measure of the
angle adjacent to the 150° angle, because I
know that the sum of the measures of two
angles that make a straight line equal 180°.
Next, I added two remote interior angles
because I know the sum of the measures of
two remote interior angles are equal to the
measure of the exterior angle.
The missing angle is 235°
Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3
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8. G.1
4. Parallelogram ABCD is shown on the coordinate plane.
A. Rotate Parallelogram ABCD 180 clockwise about the origin and plot Parallelogram EFGH on
the coordinate plane.
B. Identify the coordinates for
each image on the coordinate
plane.
Coordinates
E
F
G
H
C.
Select all the following statements about Parallelogram ABCD and Parallelogram EFGH on the
coordinate plane above that are true.
☐
☐
☐
☐ ̅̅̅̅̅
̅̅̅̅
☐ ̅̅̅̅
̅̅̅̅
☐ ̅̅̅̅
̅̅̅̅
☐ ̅̅̅̅
̅̅̅̅
☐
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8. G.3
5. Kelly and Jake are working together on the sequence of transformations that occurred on the
coordinate plane below. Kelly says that the pre-image was reflected over the y axis followed by a
reflection over the x-axis. Jake says the pre-image had to be reflected over the x-axis followed by
the a reflection over the y-axis. Kelly and Jake turn to Mark to settle the argument. Mark says
they are both right and the teacher agrees with Mark.
A. Explain how they can both be right about the sequence of transformations. You may use
words, drawings or tables to justify your explanation.
B. Ian says there is another way to describe the transformation that Kelly, Jake and Mark are
examining on the coordinate grid above. Describe another sequence or type of
transformation that would have the same results as above.
Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3
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8. G.3
6.
A. Identify the sequence of transformations that could take ∆ XYZ to ∆ X’Y’Z’
☐a reflection across the x-axis followed
by a translation of 2 units to the right
☐ a rotation 180° clockwise about the
origin followed by a translation of 7 units
up
☐ a translation of 2 units to the right
followed by a rotation 90° clockwise
about the origin
☐ a reflection across the y-axis followed
by a translation of 3 units down
8.G 2
B. Select all statements that are true about the transformation above.
☐ All congruent figures are similar because they have a scale factor of 1.
☐ All similar figures are congruent because they have a scale factor of 1.
☐ The triangles are not similar because the pre-image was dilated by a scale factor of 1.
☐ The triangles are congruent because the pre-image was dilated by a scale factor of 1.
8. G.3
Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3
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7. Apply a dilation by a scale factor of centered at the origin and record the new image’s
coordinates in the table.
Coordinates
S’
R’
Q’
8. G. 4
8. Determine if the triangles are similar. Justify your answer.
8. G.5/8. EE.7
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9.
A. Given
each angle.
and
solve for x and find the measure of
X = _______
8.G.5
10. Determine if each of these statements is always true, sometimes true, or never true.
A. A triangle can have 2 right angles.
☐ sometimes true
☐ always true
☐ never true
B. Alternate exterior angles of parallel lines cut by a transversal are congruent .
☐sometimes true
☐always true
☐ never true
C. Same side exterior angles of parallel lines cut by a transversal are supplementary.
☐sometimes true
☐always true
☐never true
D. If the measure of an angle is represented by x, then the measure of its supplement is
represented by 180-x.
☐sometimes true
☐always true
☐never true
E. If a pair of triangles has two congruent angles, the triangles are similar.
☐sometimes true
☐always true
☐never true
8. G.2
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11. A sequence of transformations was applied to an equilateral triangle in a coordinate plane. The
transformations used were rotation, reflections, and translations. Which statement about the
resulting figure is true?
☐ It must be an equilateral triangle with the same side lengths as the original triangle.
☐ It must be an equilateral triangle but the side lengths may differ from the original triangle.
☐ It may be a scalene triangle, and all the side lengths may differ from the original triangle.
☐ It may be an obtuse triangle with at least one side the same length as the original triangle.
8. G.5
12. In the figure, p ll q. Which of these statements is not true?
☐ 2 and 6 are congruent because corresponding angles are congruent.
☐ 2 and 7 are supplementary because same
side exterior angles are supplementary
☐ 6 and 5 are congruent because same side
interior angles are congruent
☐ 1 and 7 are congruent because alternate
exterior angles are congruent
☐ 3 and 5 are congruent because alternate
interior angles are congruent
☐ 4 and 5 are supplementary because same
side interior angles are supplementary
Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3
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