This activity explores (a) relationships among non-square regular polygons constructed on the sides of a right triangle and (b) visual and numerical proofs of the Pythagorean Theorem using rotations and non-square polygons.
Before the Activity
Download and make the TNS available to students. Make copies of the handouts as needed.
Students should have a basic understanding of regular polygons, area, the Pythagorean Theorem, and geometric transformations (rotations). Possible curricular placements include middle school, informal and regular geometry in high school, or geometry courses for pre-service or in-service teachers at the college level.
During the Activity
This activity is designed to be teacher led and requires minimal or no student experience with a TI-Nspire handheld device. Having students record their findings on the Student Worksheet will encourage engagement, retention, and mathematical communication. Teachers should encourage students to share their predictions and conjectures during the activity.
Oftentimes, students of all ages have memorized the formula a2 + b2 = c2 with no real understanding of how it relates to area. For those who have seen squares drawn on the sides of a right triangle, they rarely realize that squares are not the only shape for which the Pythagorean Theorem holds. A TI-Nspire handheld device enables students to explore other similar polygons drawn on the legs of a right triangle both visually and numerically.
After the Activity
After students complete this activity, they should possess a deeper understanding of how areas of various similar figures relate to the Pythagorean Theorem.