Grade 8, Unit 1 Practice Problems - Open Up Resources

8/23/2017

Grade 8, Unit 1 Practice Problems - Open Up Resources

Rigid Transformations and Congruence

Lesson 1

Problem 1

The six frames show a shape's di erent positions.

Describe how the shape moves to get from its position in each frame to the next.

Solution

To get from Position 1 to Position 2, the shape moves up. To get from Position 2 to Position 3, the shape rotates 90 degrees counterclockwise. To get from Position 3 to Position 4, the shape moves down and to the right. To get from Position 4 to Position 5 the shape rotates 90 degrees clockwise. To get from Position 5 to Position 6, the shape moves to the left.

Note: 90 degrees counterclockwise is the same as 270 degrees clockwise, and similarly 90 degrees clockwise is the same as 270 degrees counterclockwise.

Problem 2

These ve frames show a shape's di erent positions.

Describe how the shape moves to get from its position in each frame to the next.

Solution

To get from Position 1 to Position 2, the shape moves to the right. To get from Position 2 to Position 3, the shape rotates 90 degrees clockwise. To get from Position 3 to Position 4, the shape moves down. To get from Position 4 to Position 5, the shape rotates 180 degrees.

Problem 3

Diego started with this shape.



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Grade 8, Unit 1 Practice Problems - Open Up Resources

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.

Solution

Lesson 2

Problem 1

Each of the six cards shows a shape.

1. Which pair of cards shows a shape and its image after a rotation?

2. Which pair of cards shows a shape and its image after a re ection?

Solution

1. Cards 1 and 4

2. Cards 3 and 5

Problem 2

The ve frames show a shape's di erent positions.

Describe how the shape moves to get from its position in each frame to the next.

Solution



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Grade 8, Unit 1 Practice Problems - Open Up Resources

To get from Position 1 to Position 2, the shape moves to the right. To get from Position 2 to Position 3, the shape ips over a horizontal line. To get from Position 3 to Position 4, the shape moves to the left. To get from Position 4 to Position 5, the shape ips over a horizontal line again. The shape has then returned to its original position in Position 1.

Alternatively, to get from Position 1 to Position 2 or from Position 3 to Position 4, the shape may ip over a vertical line. Since the shape is symmetric, a ip looks the same as a shift here. To get from Position 2 to Position 3 or from Position 4 to Position 5, the shape may be rotated 180 degrees about a point not on the polygon.

Problem 3

(from Unit 1, Lesson 1) 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

Solution

B, E

Lesson 3

Problem 1

Apply each transformation described to Figure A. If you get stuck, try using tracing paper.

1. A translation which takes to 2. A counterclockwise rotation of A, using center , of 60 degrees 3. A re ection of A across line

Solution

1.



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Grade 8, Unit 1 Practice Problems - Open Up Resources

2.

3.

Problem 2

Here is triangle drawn on a grid.



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On the grid, draw a rotation of triangle was done.

Grade 8, Unit 1 Practice Problems - Open Up Resources , a translation of triangle , and a re ection of triangle . Describe clearly how each

Solution

Answers vary. Sample answers: The rotation is a 90-degree counterclockwise rotation using center . The translation is 4 units down and 3 to the left. The re ection is across a horizontal line through point .

Problem 3

(from Unit 1, Lesson 2) 1. Draw the translated image of

so that vertex moves to . Tracing paper may be useful.

2. Draw the re ected image of Pentagon

with line of re ection . Tracing paper may be useful.

3. Draw the rotation of Pentagon useful.

around clockwise by an angle of 150 degrees. Tracing paper and a protractor may be

Solution

1.

2.



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