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Two. If you start from any vertex, the lines to either of the two adjacent vertices will be one of the sides of the original shape. Only the line joining it to the opposite vertex will be a new line - a diagonal. Four vertices might therefore suggest four such lines but remember you're counting each line twice - once from each of its end. From any vertex, you can have only one diagonal - to the next but one vertex. Lines to the next vertex, on either

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Q: How many diagonals does a shape with 4 sides have?
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