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Math · Geometry · Unit 1

Unit 1: Constructions and Rigid Transformations

Students perform compass-and-straightedge constructions, define rigid motions (reflections, translations, rotations) without reference to a coordinate grid, describe symmetries, and use transformations to prove theorems about lines, angles, and parallel lines.

Worksheets

Every sheet has an answer key. Free to print, no login.

Unit
📝 Worksheet ✅ Answer guide
Concept
📝 Worksheet ✅ Answer key
Practice
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key
Advanced
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key

What this unit covers

A Constructions · 9 lessons
Goals
  • Create a construction from instructions.
  • Describe construction steps precisely.
  • Use circles in a construction to reason about lengths in figures.
Lessons
  1. Build It
  2. Constructing Patterns
  3. Construction Techniques 1: Perpendicular Bisectors
  4. Construction Techniques 2: Equilateral Triangles
  5. Construction Techniques 3: Perpendicular Lines and Angle Bisectors
  6. Construction Techniques 4: Parallel and Perpendicular Lines
  7. Construction Techniques 5: Squares
  8. Using Technology for Constructions (Optional)
  9. Speedy Delivery
B Defining Rigid Transformations · 5 lessons
Goals
  • Comprehend that rigid transformations produce congruent figures by preserving distance and angles.
  • Draw the result of a transformation of a given figure.
Lessons
  1. Rigid Transformations
  2. Defining Reflections
  3. Defining Translations
  4. Incorporating Rotations
  5. Defining Rotations
C Working with Rigid Transformations · 4 lessons
Goals
  • Describe the symmetries of a figure using transformations that take the figure onto itself.
  • Explain a sequence of transformations to take a given figure onto another.
Lessons
  1. Symmetry
  2. More Symmetry
  3. Working with Rigid Transformations
  4. Practicing Point-by-Point Transformations (Optional)
D Evidence and Proof · 3 lessons
Goals
  • Label diagrams in order to write precise conjectures.
  • Prove theorems about lines and angles.
Lessons
  1. Evidence, Angles, and Proof
  2. Transformations, Transversals, and Proof
  3. One Hundred Eighty
E Let’s Put It to Work · 1 lesson
Lessons
  1. Now What Can You Build? (Optional)
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.