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Math Help - Pentagon Problem

  1. #1
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    Pentagon Problem

    Hi, here is a geometry 'proof question'

    Why, in an equilateral pentagon, can there be not more than two right angles?

    Thanks for any guidance
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  2. #2
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    Quote Originally Posted by jt1894 View Post
    Hi, here is a geometry 'proof question'

    Why, in an equilateral pentagon, can there be not more than two right angles?

    Thanks for any guidance
    Let A, B, C, D, E denote the vertices of the pentagon.

    1. If you use 3 right angles at the vertices A, B, C you would get a square but not a pentagon.

    2. Therefore the right angles must be at A, B and D. To be an equilateral pentagon the triangle CDE must be an equilateral triangle too. But there doesn't exist an equilateral right triangle.
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