A visual proof of the Pythagorean theorem
by Branko Ćurgus
The first three steps of the visual proof below are as follows:
The point in the first step is the center of the corresponding square.
The line segment in the second step is parallel to the hypothenuse. Therefore its length is equal to the length of the hypothenuse. The center of the square is its midpoint.
The line segment in the in the third step is orthogonal to the hypothenuse. In fact it is the line segment from the second step rotated around the center of the square for the right angle.
Click on the image for a visual proof of the Pythagorean theorem.