Sequences of Rigid Motions on the Coordinate Plane
Written by Adi Ackerman, Head Teacher
"Sequences of Rigid Motions on the Coordinate Plane" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.G.A.2. A 7th grader who is already steady on transformations can use it too, and an older student can use it as a short review.
8th grade math worksheet: describe two rigid motions that map each figure onto its image and track where A lands after step 1. Answer key included. Part of our congruence and similarity transformations collection. Aligned to Common Core standards.
How do I use this worksheet?
Start with What Rigid Motions Preserve so students see why rigid motions make congruent figures. Move to the sequence and similarity grids, then close with the angle-angle sheets.
What students will practice
- Students will describe a sequence of two rigid motions that maps a figure onto its image.
- Students will use translations, reflections and rotations about the origin in each sequence.
- Students will write the coordinates of A after the first step.
Translate Figures on the Coordinate Plane
Rotate Figures About the Origin
Reflect Figures Across the Axes and Lines
Dilate Figures From the Origin
Describe Translations With Coordinate Rules
Describe Rotations From Before and After Graphs
Describe Reflections and Name the Line
Describe Dilations and Find the Scale Factor
Curriculum Links
Common Core State Standards
Geometry · 8th Grade
Standard: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
View all 8.G.A.2 worksheets →Find this in the curriculum
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FAQ
How do I use this congruence and similarity worksheet?
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Start with What Rigid Motions Preserve so students see why rigid motions make congruent figures. Move to the sequence and similarity grids, then close with the angle-angle sheets.
What does this worksheet teach?
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Describe two rigid motions that map each figure onto its image and track where A lands after step 1. The directions on the page read: Describe two rigid motions that map each figure onto its image (rotate about the origin only). Then write where A is after your step 1. More than one sequence can work. An answer key is included.
Can I use this congruence and similarity worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade transformations, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
What do rigid motions preserve?
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Translations, reflections and rotations keep side lengths and angle measures the same, so the image is congruent to the original. What Rigid Motions Preserve has students measure a trapezoid and its image to check.
What is angle-angle similarity?
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If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The third angles must then match too, because each triangle's angles add up to 180°.
How do you find a missing side in similar triangles?
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Match the corresponding sides, write a proportion and solve for x. Use Angle-Angle Similarity to Find Missing Sides first asks which two pairs of angles make the triangles similar.
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Worksheet Details
| Grade | 8th Grade |
| Subject | Math |
| Topic | Transformations |
| Standard | 8.G.A.2 |
| Pages | 1 page |
| Difficulty | Medium |
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Translate Figures on the Coordinate Plane
Rotate Figures About the Origin
Reflect Figures Across the Axes and Lines
Dilate Figures From the Origin
Describe Translations With Coordinate Rules
Describe Rotations From Before and After Graphs
Describe Reflections and Name the Line
Describe Dilations and Find the Scale Factor