Extension - Polygon Diagonals
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A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a triangle have? - 0
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- There are no nonadjacent vertices!
3 Angles - 3 Adjacent = 0 diagonals
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a quadrilateral have? - 2
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- 4 Angles - 3 Adjacent = 1 diagonal
1 + 1 = 2
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a pentagon have? - 5
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- Notice the math pattern below!
- 5 Angles - 3 Adjacent = 2 diagonals
2 + 2 + 1 = 5
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a hexagon have? - 9
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- Notice the math pattern below!
- 6 Angles - 3 Adjacent= 3 diagonals
3 + 3 + 2 + 1 = 9
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does an octagon have? - 20
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- Notice the math pattern below!
- 8 Angles - 3 Adjacent = 5 diagonals
5 + 5 + 4 + 3 + 2 + 1 = 20
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a heptagon have? - 14
- 7 Angles - 3 Adjacent = 4 diagonals
4 + 4 + 3 + 2 + 1 = 14
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a nonagon have? - 27
- 9 Angles - 3 Adjacent = 6 diagonals
6 + 6 + 5 + 4 + 3 + 2 + 1 = 27
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a decagon have? - 35
- 10 Angles - 3 Adjacent = 6 diagonals
7 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 35
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