While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by construction, doing a great job of reinforcing the need to take explanations back to definitions and fundamental principles. Practice with the nomenclature and mechanics of transformations is a definite plus as well.

 

Concepts

congruent triangles, transformations, rotations, reflections, translations

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Additional Tags

math

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Instructional Ideas

• Have the class create similar exercises then switch with a partner to find the series of transformations that map one shape to its image
• Plotting the images on a grid allows for the introduction of coordinate rules for the indicated transformations

Classroom Considerations

• Careful monitoring for proper naming of points in the intermediate steps will make the final step easier
• Creating a template or stencil of the triangle might help learners stuck on making the transformations exact
• Activity specifies colors in instructions which could cause confusion when using black and white copies

Pros

• Great synthesis activity for transformations, proofs, and congruence criteria
• Requires exactness in naming and following directions while providing support in building a rigorous proof

Cons

• Supplementary task link on page 2 links to general Illustrative Mathematics page, not the task or GeoGebra worksheet described
• Teacher notes / answer key are not separated from the student task

Common Core

HSG-CO.B.8