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##### Pythagoras - two approaches

Areas of squares ...or lengths of sides, squared?

Publisher: Texas Instruments UK

Editor: Barrie Galpin

Author: Allan Duncan

Topic: Mathematics

Tags Pythagoras

Pythagoras? Theorem is essentially about **areas** of shapes. It says that ?the area of the square **on** the hypotenuse equals the sum of the areas of the squares **on** the other two sides?. However, in practice, when used to find the length of sides in a right-angled triangle, the areas are ignored and we concentrate more on the value of the **square of the length** of the sides. In this sense, Pythagoras? Theorem may be re-stated as ?the square **of** the length of the hypotenuse equals the sum of the squares **of** the lengths of the other two sides?. The emphasis moves from geometry to algebra.

The tns file offers two similar approaches taken by Karen Birnie and John Slane, both of which make connections between dynamic geometry diagrams and dynamically linked measurement data from the spreadsheets. Two lessons in which the different approaches were used are described in "Inspired Connections in Maths Lessons", published in the autumn of 2010. For a pdf version of the entire booklet please click **here.**