I don't understand. Please, help
How many diagonals are there in a polygon with 9 sides?
The answer is 36

Question

I don't understand. Please, help
How many diagonals are there in a polygon with 9 sides?
The answer is 36

loser66 · Answer

With 9 nodes, we pick 2 nodes to form a diagonal, hence there is 9C2 ways to get the diagonals that is 36 ways

jim_thompson5910 · Answer

https://www.mathsisfun.com/geometry/polygons-diagonals.html

loser66 · Answer

However, with the formula $\dfrac{n(n-3)}{2}$ we get $dfrac{9(9-3)}{2}=27$ :(

jim_thompson5910 · Answer

There are n vertices. You can choose n-3 other vertices to make a segment. You cannot choose the two neighboring vertices or the original vertex itself. That's why the "n-3" is there

jim_thompson5910 · Answer

the /2 portion is to correct for double counting

loser66 · Answer

But the 2 answers didn't match. The first one is 36, the second one is 27 , how?

jim_thompson5910 · Answer

36 is incorrect. It must be a typo

jim_thompson5910 · Answer

If it asked "how many distinct line segments can be formed with 9 points?", then the answer would be 36

loser66 · Answer

question 3 http://www.testpreppractice.net/practice-tests/problem-solving-sm/pssm1.html?testname=GRE

jim_thompson5910 · Answer

maybe instead of diagonals, they just meant how many segments were possible

loser66 · Answer

They confuse me a lot. I interpreted it as above, we pick 2 vertices to form a diagonal, hence 9C2 is what they did. But the formula on your site tells me other thing. That's why I make question here.
One more thing, 9C2 is a valid logic, right?

jim_thompson5910 · Answer

or maybe they redefined "diagonal", but that doesn't make much sense really

loser66 · Answer

Ok, let me try on smaller number of sides of a polygon. Thanks for clarifying it.

loser66 · Answer

Yes, I think your site is better, just look at a rectangular. Obviously it has 2 diagonals, but if 4C2 = 6 which is total segments on a rectangular, hhehehe.!!!