Education Technology

President Garfield's Proof of the Pythagorean Theorem

Activity Overview

Students will:

  • Construct an right triangle and rotate it to create a congruent triangle, a new right angled triangle, and a trapezoid.
  • Measure side areas to observe the properties of President Garfield's construction.
  • Try to alter the properties of their construction by moving the vertices.
  • From the construction, prove the Pythagorean Theorem.
  • Before the Activity

    Provide each student with a copy of the attached .pdf document.

    During the Activity

    This activity will help students visualize the Pythagorean relationship in a very different manner. Rather than squares built off the sides of the triangle, a completely different approach is used that involves three triangles as part of a trapezoid. The algebraic proof is a very natural extension of the construction.

    After the Activity

  • Review student answers
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary