Please help!

In a quadrilateral, a student can draw two diagonals. In a pentagon, a student can draw five diagonals. In a hexagon, a student can draw nine different diagonals. How many diagonals can be drawn in a regular polygon that has 17 sides?

Question

Please help! 

In a quadrilateral, a student can draw two diagonals. In a pentagon, a student can draw five diagonals. In a hexagon, a student can draw nine different diagonals. How many diagonals can be drawn in a regular polygon that has 17 sides?

myininaya · Answer

they are trying to get you to see a pattern in the statements that come before the actual question

myininaya · Answer

4-gon (4 sider) there are 2 diagonals
5-gon (5 sider) there are 5 diagonals
6-gon (6 sider) there are 9 diagonals 
....








17-gon (17 sider) there are ? diangonals

anonymous · Answer

14?

myininaya · Answer

so lets look at a 7-gon and see if we can see a pattern emerging
or you can see if you already see a pattern in the numbers given

anonymous · Answer

Oops. My bad that would be if it was a 7-gon. Correct?

myininaya · Answer

yes for 7-gon we would have 14 diagonals

myininaya · Answer

Let me ask you a question.
For a 7-gon, there are how many vertices?

anonymous · Answer

7

myininaya · Answer

Good.
So in this picture:
|dw:1385946360793:dw|
Do you see from point A how many line segments touch it?

anonymous · Answer

Yes

myininaya · Answer

You should see the diagonals I drew from point A and also the actual 2 sides that are touching it.
There are 6 line segments touching it right?

anonymous · Answer

Yes. From left to right.

myininaya · Answer

Each of those vertices will have 6 line segments coming from it.

myininaya · Answer

And again there are 7 vertices.

myininaya · Answer

but we don't actually won't to count the sides of the shape when we count the diagonals, right?

anonymous · Answer

Yes. Only the diagonals connecting to point A?

myininaya · Answer

So right now we are looking at 7 vertices each of them having 6 line segments coming from it
7(6)=42
But we don't want to count the sides of the shape so we have 7(6)/2=42/2=21
This is still way to many.diagonals.
This means we are counting some diagonals more than once, right?

myininaya · Answer

Guess what the difference between 21 and the amount of diagonals you found is.

anonymous · Answer

So we'd only count them once to find the correct amount?

myininaya · Answer

|dw:1385946981838:dw|
This where that dividing by 2 mess came from 
7(6/2)=7(3)=21
But yes we want to count each of the diagonals one and not put them in our count more than once.
so how do we get from 21 to 14 (because 14 is actual count in diagonals where as 21 includes counting diagonals more than once)
The difference between 21 and 14 is 7, right?
But guess what is so important about 7 in this shape?
It is the number of sides right?