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.

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Concept

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Practice

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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)