Year 9 Pythagorean Semicirlces
All of us a familiar with the interpretation of Pythagoras Theorem that the sum of the areas of the squares on the two shorter sides will add up to the area of the square that is built on the hypotenuse. BUT, have you ever thought about if Pythagoras theorem would hold if we constructed different shapes on the sides of the triangle? Suppose you have a right triangle with sides a and b and hypotenuse c. Draw semicircles on each side of the triangle and find the relation among the areas of these semicircles. Describe the relationship between the two small semicircles and the largest semicircle.