Let us assume that we have a perfect square of sides (a + b) units and an inscribed square of sides c units.
We can express the area of the interior square in two different ways;
Area of square = c2Â square units. Or,
Area of square = area of the big square â€“ area of the region not taken by the small
= (a + b)2Â â€“ Â½ of4(ab)
= a2Â + 2ab +b2Â â€“ 2ab
= a2Â + b2Â square units.
Therefore, since the two algebraic expressions represent the area of the same plain figure; theyÂ mustÂ be equal, c2Â = a2Â + b2, proving Pythagoras theorem (Khalaf, 1996, p. 1).
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