Question 4297: How many diagonls can be drawn from each vertex of a decagon?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! This question can be answered either by "discovery" or by "construction."
For discovery method, consider a rectangle, which has four sides and one diagonal from a given vertex.
Next consider a pentagon, which has five sides and (picture it!) two diagonals from a given vertex.
Consider a hexagon, which has 6 sides, and each additional side adds an additional diagonal from each given vertex, which would be 3 diagonals.
Did you notice the pattern? The number of diagonals from a given vertex is 3 less than the number of vertices. The question at hand is for a decagon, which is a 10 sided figure, so there would be 10-3 or 7 diagonals from a given vertex.
Finally, you could always draw a 10 sided figure, draw all the diagonals from a given vertex, and count them for yourself!!
R^2 from SCC
|
|
|
