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Geometry for Enjoyment and Challenge

a How many diagonals does a triangle have?

b How many diagonals does a quadrilateral have?

c How many diagonals does a five-sided polygon have?

d How many diagonals does a six-sided polygon have?

e How many diagonals meet at one vertex of a polygon with $n$ sides?

f How many vertices does an n-sided polygon have?

g How many diagonals does an $n$ -sided polygon have?