Similar Triangles

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great exercise in forming logical geometric proofs. In this straightforward problem, two triangles are known to have congruent angles, and the class details the transformations necessary to map one to the other.

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CCSS: Designed
Instructional Ideas

  • Overlay triangles on a grid to introduce coordinate notation to the transformations, or to give concrete values to the abstract transformations
  • See how many different paths the class can take to show the similarity of triangle ABC to DEF
Classroom Considerations

  • Student worksheet spacing has an inconvenient page break before the diagram, which might require rearranging
  • Final page is blank, if copying costs are a consideration
  • Solution images will lose some clarity without color copies
Pros

  • Proof from basic principles justifies a frequently used similarity criteria
  • Multiple paths to correct answer
Cons

  • Teaching notes and answer key not separated from student worksheet
Common Core