Forging Connections

This site supports the NSF project on Technology-Rich Units for Future Secondary Teachers: Forging Dynamic Connections Between Geometry and Functions, which is part of the NSF's program on Improving Undergraduate STEM Education (IUSE).

Unit 3: Formalize Congruence and Similarity

  1. Prove Segment Congruence: The student constructs transformations that superpose one segment on another of equal length so that the construction remains valid no matter how the segments are repositioned. The student then uses the construction to formulate a proof of the Segment Congruence Theorem.
  2. Prove the SSS Theorem: After reviewing the definition of reflection and the Perpendicular Bisector Theorem, the student transforms one of two triangles having the same side lengths. The transformation superposes the image of one triangle on the other triangle, and the construction forms the basis for the student's proof.