Similar Triangles and the Pythagorean TheoremDerive the Pythagorean Theorem by eliminating the x.I have already shown that △ B A E and △ B D E are congruent, and that △ E D C and △ B A C are similar triangles. However, I am having trouble setting up the resulting proportions and using that to derive the Pythagorean Theorem. I believe the resulting proportions are B A D E = A C D C = B C E C ..Any help will be appreciated!

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Similar Triangles and the Pythagorean TheoremDerive the Pythagorean Theorem by eliminating the x.I have already shown that   △  B  A  E and   △  B  D  E are congruent, and that   △  E  D  C and   △  B  A  C are similar triangles. However, I am having trouble setting up the resulting proportions and using that to derive the Pythagorean Theorem. I believe the resulting proportions are            B      A              D      E        =            A      C              D      C        =            B      C              E      C        ..Any help will be appreciated!

se4neto34yt · Accepted Answer

Since   B  E is the angle bisector of                     A        B        C            ^       we have that  A  E  =      c          a      +      c        ⋅  b  ,    C  E  =      a          a      +      c        ⋅  band since             C      D              C      E        =      b    a   we also have  a  =  C  D  +  B  D  =      b    a    C  E  +  A  B  =      b    a    ⋅            a      b              a      +      c        +  cfrom which:  (  a  −  c  )  (  a  +  c  )  =      b    2  and       a    2    =      b    2    +      c    2   as wanted.

Similar Triangles and the Pythagorean Theorem 04220400491.jpg Derive the Pythagorean Theorem

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