• A New Way to Build a Geometric System

    by  • July 17, 2013 • Math • 0 Comments

    This is a quick preview, I will expand upon it when I can.

    Here is the outline of another approach to the beginning of Geometry, where each major step can be observed through software or manipulatives, since they are visually obvious, or demonstrated through coordinate geometry. Some must be postulates, others can then be proven.

    1. Translations, Rotations, and Reflections are isometries, that is, they maintain size and shape.

    2. Congruent figures are defined as the result of isometries.

    3. CPCTC, including altitudes.

    4. Put [1] – [3] together. Each triangle in the figure below is a rotation about the midpoint of the adjacent side.

    Screen Shot 2013-07-17 at 10.32.07 PM

    5. Lines equidistant at 2 places are equidistant everywhere.

    6. Equidistant lines are defined as parallel.

    7. Angle pairs formed by parallel lies intersected by a transversal can be explored, and their relationships proven, by constructing and transforming appropriate figures.

    Video Proof 1 copy OK, so that’s my thinking. What do you think? Please let me know!


    After teaching for 14 years, I now design curriculum and create digital and print instructional materials for high school and middle school math. I have also invented and am now marketing radian-scale protractors. Check out www.proradian.net! I'm very happily married and have 2 grown sons and a cat named Louie.

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