Deduce the Pythagorean Theorem [duplicate]Let V be an inner product space,and suppose that x and y are orthogonal vectors in V.We also know ‖ x + y ‖ 2 = ‖ x ‖ 2 + ‖ y ‖ 2 .My question is how can we deduce the pythagorean theorem in R 2 from it.If possible give geometrical views.Any help will be greatly appreciated.thanks!! in advance.

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Deduce the Pythagorean Theorem [duplicate]Let V be an inner product space,and suppose that x and y are orthogonal vectors in V.We also know             ‖      x      +      y      ‖        2    =            ‖      x      ‖        2    +            ‖      y      ‖        2  .My question is how can we deduce the pythagorean theorem in             R        2   from it.If possible give geometrical views.Any help will be greatly appreciated.thanks!! in advance.

Ashlynn Mcmillan · Accepted Answer

Use the standard inner product space with             R      2      . Then       ‖    x    ‖   is the length of x,       ‖    y    ‖   is the length of y, and       ‖    x    +    y    ‖   is the length of the diagonal connecting x and y. In this case then,             ‖      x      +      y      ‖        2    =            ‖      x      ‖        2    +            ‖      y      ‖        2   is equivalent to the pythagorean theorem in             R        2  .

Deduce the Pythagorean Theorem [duplicate] Let V be an inner product space,and suppose that x and y

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