23.3.1. Finding Number of Diagonals

Try these first

1. 1.

   How many diagonals does a triangle have?

   Hint

   Remember a triangle has no non-adjacent vertices.

2. 2.

   Calculate the number of diagonals in a square.

   Hint

   Use the formula with n = 4.

3. 3.

   How many diagonals does a pentagon have?

   • 5
   • 10
   • 15

   Hint

   Think about the formula for diagonals.

4. 4.

   True or False: A triangle has diagonals.

   • True
   • False

   Hint

   Consider what defines a diagonal.

5. 5.

   If a polygon has 12 sides, calculate the number of diagonals and describe the relationship between the number of sides and diagonals.

   Hint

   Remember the formula and notice the pattern in diagonal counts.

6. 6.

   Explain how the diagonal formula could be extended to non-convex polygons and the considerations you would need to make.

   Hint

   Think about how non-adjacency applies in different polygon types.