COURSE 2 LESSON 7-6
Draw a Diagram and Look for a Pattern
How many diagonals can be drawn inside a decagon?
The goal is to find the number of diagonals that can be drawn inside a
decagon.
Remember that a diagonal is a segment that joins two vertices that are
not endpoints of the same side of a polygon.The diagram below shows
all the diagonals that can be drawn inside each polygon shown.
3 sides
4 sides
5 sides
7-6
6 sides
COURSE 2 LESSON 7-6
Draw a Diagram and Look for a Pattern
(continued)
Make a table to organize the information from the diagram.
sides
diagonals
3
0
4
2
5
5
6
9
The data in the table indicates that the formula for the number of
diagonals that can be drawn inside a polygon of n sides is n(n – 3)
2
For a decagon, n = 10.
10(10 – 3) 10 • 7
= 2 = 35
2
Thirty-five diagonals can be drawn inside a decagon.
7-6
COURSE 2 LESSON 7-6
Draw a Diagram and Look for a Pattern
(continued)
To check that 35 diagonals can be
drawn inside a decagon, draw a diagram.
There are 35 diagonals.
7-6
COURSE 2 LESSON 7-6
Draw a Diagram and Look for a Pattern
Solve by drawing a diagram and looking for a pattern.
The exterior angles of a triangle are the supplements of the interior
angles, as shown. What is the sum of the exterior angles of a
regular hexagon?
360º
7-6