Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Transformational Geometry
• Math: Geometry: Triangles

9-12

50 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
Visit TI Math.com.

## 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.