Because the angle BCE is 90 degrees, the angle BCA+ the angle ECD=90 degrees.

Angle BCA+ angle ABC=90 degrees, so angle ABC= angle ECD.

According to the corner theorem, it can be proved that △ ABC △ DCE

Let AB = A, AC = B, BC = Ce = C, then CD = A, ED = B, AD = A+B.

S△ABC+S△CDE+S△BCE= trapezoidal Abed

ab/2+ab/2+cc/2=(a+b)(a+b)/2

cc/2=(aa+bb)/2

cc=aa+bb

pythagorean theorem