Euclid's Proof of Pythagorean Theorem

Let the yellow triangle be a right triangle. Show that the sum of the areas of the blue and green squares equals the area of the red square. Verify the following:

• Notice that triangles ABD and CDF are congruent (identical)
• Area of triangle CDF = one-half the area of the blue square
• Area of triangle ABD = one-half the area of rectangle AGED
• Therefore, area of the blue square = area of rectangle AGED
• Surmise that a similar analysis will show that the area of the green square = area of rectangle GHFE
• And therefore, that the sum of the areas of the blue and green squares equals the area of the red square

Since the area of each square = the square of the corresponding side of the yellow triangle, the theorem of Pythagoras is proved.