RIDGE

Triangle Square Triangle Problem

Description:	Source(s):
ABC est un triangle quelconque. A l’extérieur du triangle, trois carrés ont été construits sur chacun des trois côtés. On construit trois nouveaux triangles en reliant les sommets libres des carrés. Comparer l’aire de chacun des trois triangles avec l’aire du triangle ABC.	(Pedemonte 2002, thèse)
ABC is a triangle. Three exteriors squares are constructed on the triangle’s sides. The free points of the squares are connected defining three other triangles. Compare the areas of these triangles with the area of triangle ABC (see figure).	(Pedemonte 2003, CERME)

Prior knowledge 

Prior DGS content required:

• Construction of square
• Area measure

Prior mathematical content required:

• Basic geometry

Prior mathematical content related:

• Trangle area
• Rotation

Possible learning

Likely DGS content learned:

• Rotation tool

Possible solutions

In a dynamic geometry environment it is simple to discover that the areas of all four triangles are the same.  The problem is then to prove or explain this. One approach is to rotate an outer triangle 90 degrees around the vertex it shares with the inner triangle. It is then easy to see that the two triangles have the same height and same base, and hence the same area.

Supported by a research grant from the Social Sciences and Humanities Research Council of Canada

Page last updated July 2008 by David Reid