Reflection: Grappling with Complexity Rigid Motion, Congruent Triangles, and Proof - Section 1: Using Rigid Motion to Prove Triangles are Congruent


There are some things about proof by rigid motion that I consider sketchy. For instance, Just because we can find a composition of isometries that map these 2 triangles onto one another does not seem to prove to me that it works in all cases. For example, I could find two triangles that seem to map onto one another just fine, given that two sides and a non-included angle are congruent, but this definitely does not guarantee that SSA works in all cases.  I have voiced this opinion to a few people whom I consider to be knowledgeable, and was told that we should use rigid motion as an aid in helping students to visualize and to understand concepts that we had previously simply postulated, and that my reservations are warranted.  

  Rigid Motions, Proofs, and Puzzled Faces
  Grappling with Complexity: Rigid Motions, Proofs, and Puzzled Faces
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Rigid Motion, Congruent Triangles, and Proof

Unit 5: Polygons and Congruent Triangle Proofs
Lesson 1 of 6

Objective: SWBAT identify the reasons that triangles are congruent, using SAS, ASA, SSS, and AAS, by closely examining diagrams and "givens."

Big Idea: Using the method of flow chart proofs, students begin to develop the skills necessary to understand and create congruent triangle proofs.

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