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Math Help - Equilateral polygons and right angles

  1. #1
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    Equilateral polygons and right angles

    Help, I cannot draw this shape from its description:

    1) Draw an equilateral right pentagon, with exactly 1 right angle and has at least one line of symmetry.

    And I don't know how to prove this:

    2) Explain why any equilateral right pentagon (i.e including the one above) cannot have more than two right angles??

    Please help.
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  2. #2
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    Quote Originally Posted by jt1894 View Post
    Help, I cannot draw this shape from its description:

    1) Draw an equilateral right pentagon, with exactly 1 right angle and has at least one line of symmetry.

    ...
    Let a denote the length of the side.

    1. Draw the axis of symmetry.
    2. Draw an angle of 45 to both sides of the axis. The legs of these 2 angles are a.
    3. Draw parallels at both sides of the axis of symmetry in a distance of \frac12 a.
    4. Draw a circle with radius r = a from the endpoints of the legs of the 45-legs.
    5. The points of intersection of these two circles and the parallels are the two missing vertices of the pentagon.
    Attached Thumbnails Attached Thumbnails Equilateral polygons and right angles-reg5gon_mitrw.png  
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