Question: What is Pythagoras Theorem ?


Pythagoras was a Greek mathematician who lived around 500BC and discovered a significant fact about right-angled triangles known as his theorem. The area of the square on the side opposite to the right angle is equal to the sum of the areas of the squares on the sides forming the right angle.

Area C = area A + area B which is equivalent to c2 = a2 + b2
where a, b and c are the lengths of the sides of the triangle.

For example, the tiling pattern of right-angled triangles has square R and square Q each made from 4 tiles while square P is made from 8 tiles.

It is also true that whenever the lengths a, b, c of the sides of a triangle satisfy the relation c2 = a2 + b2 then the triangle is right-angled. This is the converse of pythagoras' theorem.

For example,
when a = 3, b = 4 and c = 5 then a2 + b2 = 32 + 42 = 25 = 52 = c2 and the triangle is right-angled.