Unit 1: Rigid Transformations and Congruence

Students explore translations, rotations, and reflections of plane figures in order to understand the structure of rigid transformations, and use the properties of rigid transformations to formally define what it means for shapes to be congruent.

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Concept

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What this unit covers

A Rigid Transformations · 5 lessons

Goals

• Determine coordinates that represent the image of a polygon or line segment in the coordinate plane after a transformation.
• Draw and label the image of figures that result from translations, rotations, and reflections on a square or isometric grid.
• Explain the sequence of transformations that takes one figure to its image.

Lessons

1. Moving in the Plane
2. Naming the Moves
3. Making the Moves
4. Coordinate Moves
5. Describing Transformations

B Properties of Rigid Transformations · 4 lessons

Goals

• Draw and label rigid transformations of lines and parallel lines and explain the relationship between the original and its image under the transformation.
• Identify a rigid transformation using a drawing of a figure and its image.
• Identify side lengths and angles that have equivalent measurements in composite shapes and explain why they are equivalent.

Lessons

1. No Bending or Stretching
2. Rotation Patterns
3. Moves in Parallel
4. Composing Figures

C Congruence · 2 lessons

Goals

• Compare and contrast side lengths, angle measures, and other features of shapes using rigid transformations to explain why a shape is or is not congruent to another.
• Justify that two polygons on a grid are congruent using the definition of congruence in terms of rigid transformations.

Lessons

1. What Is the Same?
2. Congruence

D Angles in a Triangle · 3 lessons

Goals

• Calculate angle measures using alternate interior, vertical, and supplementary angles to solve problems.
• Generalize that the sum of angles in a triangle is 180 degrees using rigid transformations or the congruence of alternate interior angles of parallel lines cut by a transversal.

Lessons

1. Alternate Interior Angles
2. Adding the Angles in a Triangle
3. Parallel Lines and the Angles in a Triangle

E Drawing Polygons with Given Conditions · 3 lessons

Goals

• Draw triangles with two given angle measures and one side length, one given angle measure and two side lengths, or three side lengths.
• Justify whether 3 measures of angles or sides determine a unique triangle or more than one triangle, or if no triangle is possible.

Lessons

1. Building Polygons
2. Drawing Triangles (Part 1)
3. Drawing Triangles (Part 2)

F Let's Put It to Work · 1 lesson

Lessons

1. Rotate and Tessellate (Optional)