Title: Assignment: (Task) Origami Equilateral Triangle
Course: HBUHSD Geometry Resource Course

Estimated Time: 20 minutes with discussion

Teacher Notes: The purpose of this task is to explore reflections in the context of paper folding. Each fold is associated with a line of reflection and understanding each step in the construction requires careful analysis of angles and of the properties of reflections.

Origami is a great source of problems for developing geometric intuition, cultivating artistic skills, and also for careful mathematical reasoning about reflections. Although the main alignment for this task is G-CO.12, all work with origami also relates to G-CO.A, ''Experiment with Transformations of the Plane,'' and G-SRT.5, ''Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.'' Although students do not need origami paper in order to work on this task, it would definitely be beneficial to have some paper squares with which to experiment. A variety of approaches are possible, with two presented in the solutions and a separate method is discussed below in the commentary. Work like this with origami can be done either before or after formal work with geometric proofs: if done before, it can serve as motivation and afterward it provides a rich source of examples for proving geometric theorems.

Origami Equilateral Triangle.pdf

Teacher Commentary and Solutions