Extension - Polygon Diagonals

A diagonal is a line segment that connects two nonadjacent vertices of a polygon. How many diagonals does a triangle have?
1. 0
3. 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?
1. 2
3. 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?
1. 5
3. Notice the math pattern below!
4. 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?
1. 9
3. Notice the math pattern below!
4. 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?
1. 20
3. Notice the math pattern below!
4. 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?
1. 14
2. 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?
1. 27
2. 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?
1. 35
2. 10 Angles - 3 Adjacent = 6 diagonals
  7 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 35