Here ABC, B'AE, A'B'C', and BA'D are congruent right triangles with corresponding vertices each written in the same order, C is on the line AE, E is on the line B'C', and C' is on the line A'D.

       
          A
             
             
          C    D     B


    B'    E    C'
             
             
               A' 

Explain how the same theorem has a proof that utilizes the following figure.

Here ABC is a right triangle and CF is it's altitude.

       C


    A  F         B