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Math Help - Diagonals in a regular pentagon

  1. #1
    Junior Member Nadeshiko's Avatar
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    Diagonals in a regular pentagon

    How many diagonals does a regular pentagon have?

    Please help me on this problem! I would appreciate steps on how to get the answer or hints!
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    Re: Diagonals in a regular pentagon

    A pentagon is a polygon that have five sides. a diagonal in a polygon is the line that joins any two vertices. The best you to get your answer is to sketch a pentagon and draw the diagonals. How many diagonal you will count?
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    Re: Diagonals in a regular pentagon

    Quote Originally Posted by Nadeshiko View Post
    How many diagonals does a regular pentagon have? Please help me on this problem! I would appreciate steps on how to get the answer or hints!
    A pentagon has five vertices no three of which are collinear.
    So 5 choose 2 is the number of line segments the vertices determine.
    There are five edges. The rest are diagonals.

    This process will work for any polygon.
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  4. #4
    Junior Member Nadeshiko's Avatar
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    Re: Diagonals in a regular pentagon

    Quote Originally Posted by votan View Post
    A pentagon is a polygon that have five sides. a diagonal in a polygon is the line that joins any two vertices. The best you to get your answer is to sketch a pentagon and draw the diagonals. How many diagonal you will count?
    I got 4 diagonal lines. Is that the answer?
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    Re: Diagonals in a regular pentagon

    Quote Originally Posted by Nadeshiko View Post
    I got 4 diagonal lines. Is that the answer?
    You missed one diagonal, redraw the figure and find out which one you missed.
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  6. #6
    Junior Member Nadeshiko's Avatar
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    Re: Diagonals in a regular pentagon

    I redrew the figure and I still got 4 diagonal lines. I tried 4 or 5 times and did it separately and compared my answers and I still got the same number of diagonal lines.
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    Re: Diagonals in a regular pentagon

    Quote Originally Posted by Nadeshiko View Post
    I redrew the figure and I still got 4 diagonal lines. I tried 4 or 5 times and did it separately and compared my answers and I still got the same number of diagonal lines.
    Hint: You should get a star with five spikes
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  8. #8
    Junior Member Nadeshiko's Avatar
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    Re: Diagonals in a regular pentagon

    Quote Originally Posted by votan View Post
    Hint: You should get a star with five spikes
    I got it!!!
    I got a star in the pentagon!! Thanks!
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