Now consider the two triangles Δ ABC and Δ ACH, these two triangles are similar to each other because of AA similarity. This is because both the triangle have a right angle and one common angle at A. So by these similarity, ac = ea and bc = db a2 = c*e and b2 = c*d Sum the a2 and b2, we get a2 + b2 = c*e + c*d a2 + b2 = c(e + d) a2 + b2 = c2 (since e + d = c) Hence Proved. Euclid Proof of Pythagorean Theorem According to Euclid, if the triangle had a right angle (90 degree), the area of the square formed with hypotenuse as the side will be equal to the sum of the area of the squares formed with the other two sides as the side of the squares. From the above figure 3, the sum of the area covered by the two small squares is equal to the area of the third square. Here, a2 is the area of the square ABDE, b2 is the area of the square BCFG and c2 is the area of the square ACHI.
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