Question 580521: How many triangles are formed by the diagonals from one vertex of a regular octagon? I know the answer is 6 but why isnt it 8?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Each diagonal is simply a line segment that connects two vertices of the octagon (and these segments aren't side lengths or edges).
There are 8 vertices total, which makes you think there should be 8 diagonals; however, if you pick a vertex at random, the two vertices that are adjacent to that chosen vertex are NOT included when forming the diagonal.
Why? Because drawing a line from that chosen vertex to either adjacent vertex forms a side length or edge, which is NOT a diagonal.
So there are 2 segments excluded and there are 8 - 2 = 6 diagonals stemming from one vertex.
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