[Test.3] Euclid's elegant proof of the Pythagorean theorem depends upon the diagram of Figure below, sometimes referred to as the Fanciscan's cowl or as the bride's chair.

   A precis of the proof runs as ? (AC)² = 2กโJAB = 2กโCAD = ADKL. Similarly, (BC)² = BEKL and so on. Fill in the detail of this proof.