Which construction can you use to prove the pythagorean theorem based on similarity of triangles?

To prove the Pythagorean Theorem based on similarity of triangles, you can always use the 2nd construction.

The 2nd construction is achieved by drawing a perpendicular line joining between the right angle of the triangle and the hypothesis (as shown in the attachment).

Note: The Pythagorean Theorm is stated as follows:
(length of hypotenuse)^2  = (length of side1)^2 + (length of side2)^2

They are like other investigations? say there was a murder u have to do blood test and finger prints which run through a lab.