GRADE 8 MATHEMATICS
Unit 1
Practice Problems
Rigid Transformations and Congruence
Click on a title in the list below to scroll directly to that lesson.
Lesson 1: Moving in the Plane
Lesson 2: Naming the Moves
Lesson 3: Grid Moves
Lesson 4: Making the Moves
Lesson 5: Coordinate Moves
Lesson 6: Describing Transformations
Lesson 7: No Bending or Stretching
Lesson 8: Rotation Patterns
Lesson 9: Moves in Parallel
Lesson 10: Composing Figures
Lesson 11: What Is the Same?
Lesson 12: Congruent Polygons
Lesson 13: Congruence
Lesson 14: Alternate Interior Angles
Lesson 15: Adding the Angles in a Triangle
Lesson 16: Parallel Lines and the Angles in a Triangle
Lesson 17: Rotate and Tessellate
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 1
Practice Problems
1. The six frames show a shape's different positions.
Describe how the shape moves to get from its position in each frame to the next.
2. These five frames show a shape's different positions.
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Lesson 1: Moving in the Plane 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Describe how the shape moves to get from its position in each frame to the next.
3. Diego started with this shape.
Diego moves the shape down, turns it 90 degrees clockwise, then moves the shape to
the right. Draw the location of the shape after each move.
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Lesson 1: Moving in the Plane 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 2
Practice Problems
1. Each of the six cards shows a shape.
a. Which pair of cards shows a shape and its image after a rotation?
b. Which pair of cards shows a shape and its image after a reflection?
2. The five frames show a shape's different positions.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 2: Naming the Moves 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Describe how the shape moves to get from its position in each frame to the next.
3. The rectangle seen in Frame 1 is rotated to a new position, seen in Frame 2.
Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame
2.
A. 40 degrees clockwise
B. 40 degrees counterclockwise
C. 90 degrees clockwise
D. 90 degrees counterclockwise
E. 140 degrees clockwise
F. 140 degrees counterclockwise
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Lesson 2: Naming the Moves 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 3
Practice Problems
1. Apply each transformation described to Figure A. If you get stuck, try using tracing
paper.
a. A translation which takes to
b. A counterclockwise rotation of A, using center , of 60 degrees
c. A reflection of A across line
2. Here is triangle drawn on a grid.
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Lesson 3: Grid Moves 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
On the grid, draw a rotation of triangle ,a
translation of triangle , and a reflection of
triangle . Describe clearly how each was done.
3. a. Draw the translated image of so that vertex moves to . Tracing paper
may be useful.
b. Draw the reflected image of Pentagon with line of reflection . Tracing
paper may be useful.
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Lesson 3: Grid Moves 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
c. Draw the rotation of Pentagon around clockwise by an angle of 150
degrees. Tracing paper and a protractor may be useful.
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Lesson 3: Grid Moves 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 4
Practice Problems
1. For each pair of polygons, describe a sequence of translations, rotations, and
reflections that takes Polygon P to Polygon Q.
a.
b.
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Lesson 4: Making the Moves 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
c.
2. Here is quadrilateral and line .
Draw the image of quadrilateral after reflecting it across line .
3. Here is quadrilateral .
Draw the image of quadrilateral after each rotation using as center.
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Lesson 4: Making the Moves 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
a. 90 degrees clockwise
b. 120 degrees clockwise
c. 30 degrees counterclockwise
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Lesson 4: Making the Moves 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 5
Practice Problems
1. a. Here are some points.
What are the coordinates of , , and after a translation to the right by 4 units
and up 1 unit? Plot these points on the grid, and label them , and .
b. Here are some points.
What are the coordinates of , , and after a reflection over the -axis? Plot
these points on the grid, and label them , and .
c. Here are some points.
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Lesson 5: Coordinate Moves 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
What are the coordinates of , , and after a rotation about by 90 degrees
clockwise? Plot these points on the grid, and label them , and .
2. Describe a sequence of transformations that takes trapezoid A to trapezoid B.
3. Reflect polygon using line .
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 5: Coordinate Moves 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 5: Coordinate Moves 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 6
Practice Problems
1. Here is Trapezoid A in the coordinate plane:
a. Draw Polygon B, the image of A, using the -axis as the line of reflection.
b. Draw Polygon C, the image of B, using the -axis as the line of reflection.
c. Draw Polygon D, the image of C, using the -axis as the line of reflection.
2. The point is rotated 180 degrees counterclockwise using center . What are
the coordinates of the image?
A.
B.
C.
D.
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Lesson 6: Describing Transformations 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
3. Describe a sequence of transformations for which Triangle B is the image of Triangle A.
4. Here is quadrilateral .
Draw the image of quadrilateral after each transformation.
a. The translation that takes to .
b. The reflection over segment .
c. The rotation about point by angle , counterclockwise.
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Lesson 6: Describing Transformations 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 7
Practice Problems
1. Is there a rigid transformation taking Rhombus P to Rhombus Q? Explain how you
know.
2. Describe a rigid transformation that takes Triangle A to Triangle B.
3. Is there a rigid transformation taking Rectangle A to Rectangle B? Explain how you
know.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 7: No Bending or Stretching 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
4. For each shape, draw its image after performing the transformation. If you get stuck,
consider using tracing paper.
a. Translate the shape so that
goes to .
b. Rotate the shape 180 degrees
counterclockwise around .
c. Reflect the shape over the line
shown.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 7: No Bending or Stretching 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 8
Practice Problems
1. For the figure shown here,
a. Rotate segment around point .
b. Rotate segment around point .
c. Rotate segment around point .
2. Here is an isosceles right triangle:
Draw these three rotations
of triangle together.
a. Rotate triangle 90
degrees clockwise
around .
b. Rotate triangle 180
degrees around .
c. Rotate triangle 270
degrees clockwise
around .
3. Each graph shows two polygons and . In each case, describe a
sequence of transformations that takes to .
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Lesson 8: Rotation Patterns 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
a.
b.
4. Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree
with Lin? Explain your reasoning.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 8: Rotation Patterns 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 9
Practice Problems
1. a. Draw parallel lines and .
b. Pick any point . Rotate 90 degrees clockwise around .
c. Rotate 90 degrees clockwise around .
d. What do you notice?
2. Use the diagram to find the measures of each angle. Explain your reasoning.
a.
b.
c.
3. Points and are plotted on a line.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 9: Moves in Parallel 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
a. Find a point so that a 180-degree rotation
with center sends to and to .
b. Is there more than one point that works for
part a?
4. In the picture triangle is an image of triangle after a rotation. The center
of rotation is .
a. What is the length of side ? Explain how you know.
b. What is the measure of angle ? Explain how you know.
c. What is the measure of angle ? Explain how you know.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 9: Moves in Parallel 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
5. The point is rotated 180 degrees counterclockwise using center . What are
the coordinates of the image?
A.
B.
C.
D.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 9: Moves in Parallel 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 10
Practice Problems
1. Here is the design for the flag of Trinidad and Tobago.
“The Flag of Trinidad and Tobago” via Wikimedia Commons. Public Domain.
Describe a sequence of translations, rotations, and reflections that take the lower left
triangle to the upper right triangle.
2. Here is a picture of an older version of the flag of Great Britain. There is a rigid
transformation that takes Triangle 1 to Triangle 2, another that takes Triangle 1 to
Triangle 3, and another that takes Triangle 1 to Triangle 4.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 10: Composing Figures 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
“Flag of Great Britain (1707–1800)” by Hoshi via Wikimedia Commons. Public Domain.
a. Measure the lengths of the sides in Triangles 1 and 2. What do you notice?
b. What are the side lengths of Triangle 3? Explain how you know.
c. Do all eight triangles in the flag have the same area? Explain how you know.
3. a. Which of the lines in the picture is parallel to line ? Explain how you know.
b. Explain how to translate, rotate or reflect line to obtain line .
c. Explain how to translate, rotate or reflect line to obtain line .
4. Point has coordinates . After a translation 4 units left, a reflection across the
-axis, and a translation 2 units down, what are the coordinates of the image?
5. Here is triangle :
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 10: Composing Figures 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Draw these three rotations of triangle together.
a. Rotate triangle 90 degrees clockwise around .
b. Rotate triangle 180 degrees around .
c. Rotate triangle 270 degrees clockwise around .
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 10: Composing Figures 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 11
Practice Problems
1. If two rectangles have the same perimeter, do they have to be congruent? Explain how
you know.
2. Draw two rectangles that have the same area, but are not congruent.
3. For each pair of shapes, decide whether or not it appears that the two shapes are
congruent. Explain your reasoning.
a.
b.
4. a. Reflect Quadrilateral A over the -axis. Label the image quadrilateral B. Reflect
Quadrilateral B over the -axis. Label the image C.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 11: What Is the Same? 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
b. Are Quadrilaterals A and C congruent? Explain how you know.
5. The point is rotated 90 degrees counterclockwise using center . What are
the coordinates of the image?
A.
B.
C.
D.
6. Describe a rigid transformation that takes Polygon A to Polygon B.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 11: What Is the Same? 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 11: What Is the Same? 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 12
Practice Problems
1. a. Show that the two pentagons are congruent.
b. Find the side lengths of and the angle measures of .
2. For each pair of shapes, decide whether or not the two shapes are congruent. Explain
your reasoning.
a.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 12: Congruent Polygons 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
b.
c.
3. a. Draw segment .
b. When is rotated around point , the resulting segment is the same as
. Where could point be located?
4. Here is trapezoid .
Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigid
transformations you used.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 12: Congruent Polygons 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 13
Practice Problems
1. Which of these four figures are congruent to the top figure?
2. These two figures are congruent, with corresponding points marked.
a. Are angles and congruent? Explain your reasoning.
b. Measure angles and to check your answer.
3. Here are two figures.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 13: Congruence 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Show, using measurement, that these two figures are not congruent.
4. Each picture shows two polygons, one labeled Polygon A and one labeled Polygon B.
Describe how to move Polygon A into the position of Polygon B using a transformation.
a.
b.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 13: Congruence 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
c.
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Lesson 13: Congruence 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 14
Practice Problems
1. Use the diagram to find the measures of each angle. Explain your reasoning.
a.
b.
c.
2. Lines and are parallel, and the measure of angle is 19 degrees.
a. Explain why the measure of angle is 19 degrees. If you get stuck, consider
translating line by moving to .
b. What is the measure of angle ? Explain.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 14: Alternate Interior Angles 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
3. The diagram shows three lines with some marked angle measures.
Find the missing angle measures marked with question marks.
4. The two figures are scaled copies of each other.
a. What are some ways that you can tell they are scaled copies?
b. What is the scale factor that takes Figure 1 to Figure 2?
c. What is the scale factor that takes Figure 2 to Figure 1?
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 14: Alternate Interior Angles 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 15
Practice Problems
1. In triangle , the measure of angle is .
a. Give possible measures for angles and if triangle is isosceles.
b. Give possible measures for angles and if triangle is right.
2. For each set of angles, decide if there is a triangle whose angles have these measures in
degrees:
a. 60, 60, 60
b. 90, 90, 45
c. 30, 40, 50
d. 90, 45, 45
e. 120, 30, 30
If you get stuck, consider making a line segment. Then use a protractor to measure
angles with the first two angle measures.
3. Angle in triangle is obtuse. Can angle or angle be obtuse? Explain your
reasoning.
4. For each pair of polygons, describe the transformation that could be applied to Polygon
A to get Polygon B.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 15: Adding the Angles in a Triangle 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
a.
b.
c.
5. On the grid, draw a scaled copy of quadrilateral using a scale factor of .
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 15: Adding the Angles in a Triangle 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 15: Adding the Angles in a Triangle 3
GRADE 8 MATHEMATICS
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Unit 1, Lesson 16
Practice Problems
1. For each triangle, find the measure of the missing angle.
2. Is there a triangle with two right angles? Explain your reasoning.
3. In this diagram, lines and are parallel.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 16: Parallel Lines and the Angles in a Triangle 1
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Angle measures and angle measures .
a. What is ?
b. What is ?
c. What is ?
4. The two figures are congruent.
a. Label the points , and that correspond to , , and in the figure on the
right.
b. If segment measures 2 cm, how long is segment ? Explain.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 16: Parallel Lines and the Angles in a Triangle 2
GRADE 8 MATHEMATICS
NAME DATE PERIOD
c. The point is shown in addition to and . How can you find the point that
corresponds to ? Explain your reasoning.
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 16: Parallel Lines and the Angles in a Triangle 3
GRADE 8 MATHEMATICS
NAME DATE PERIOD
Unit 1, Lesson 17
Practice Problems
Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org
Lesson 17: Rotate and Tessellate 1
