Activity Overview
A short investigation involving squares and triangles that leads to simple proof of Pythagoras's theorem. A beautiful illustration of the power of the Geometry environment and CAS functionality of TI-Nspire.
Objectives
Students use the dynamic nature of the geometry environment to build an interactive visual that easily yields an expression for Pythagoras's theorem. The CAS functionality of the calculator takes care of all the simplifications making the content much more accessible.
Vocabulary
- Pythagoras
- Triangle
- Square
- Expression
- Formula
About the Lesson
Students use the Geometry application to inscribe a square inside another square. This created four congruent triangles. Students measuare the area of the outer and inner squares and also the triangles. They construct an equation relating the squares and triangles and test their relationship on a few different sizes. This approach relies on some simple arithmetic before the slightly more complicated generalisation. The CAS functionality of the calcultor simplifies the expression entered by students and voila, Pythagoras's theorem pops out!