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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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 Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. c. Draw the rotation of Pentagon around clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org Lesson 3: Grid Moves 2 GRADE 8 MATHEMATICS NAME DATE PERIOD Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org Lesson 4: Making the Moves 2 GRADE 8 MATHEMATICS NAME DATE PERIOD a. 90 degrees clockwise b. 120 degrees clockwise c. 30 degrees counterclockwise Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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. Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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 . Unit 1: Rigid Transformations and Congruence Download for free at openupresources.org 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.