Geometry Question. I have to draw and state all the diagonals in this 8 sided polygon.?

Question

It starts with W and it's diagonal to T. X is diagonal to Q. R is diagonal to S, V is diagonal to O. I am not sure what my instructor is asking me to do.

Answer 1

He is asking you to make a pretty picture, which if you do this right, you will get. I don't get the hang of the nomenclature for the polygon, but consider another called ABCDEFGH. From A, you draw a diagonal to C, to D, to E, to F and to G. Note that you DONT draw AB or AH, since they are sides. Then from B, you draw a diagional to D, to E, to F, to G, and to H. Then from C, draw a diagonal to E, F, G and H. You DONT draw CA, because you have already drawn AC. Continue around to point G and enjoy the result.

Answer 2

Probably not enough info to answer, but...

For a polygon of N sides, there is an equation for how many diagonals there are...assuming a diagonal means a line connecting non-adjacent corners.

For a triangle, there are no diagonals 3->0
For a rectangle, there are 2 diagonals 4->2
for a pentagon, there are 5, 5->5
etc.

for n-sides, there are n-2 more than for n-1 sides

giving something like

P(n) has (n-2) * n / 2 diagonals

An 8-sided polygon would then have

(8-2)*8/2 = 24 diagonals.

Answer 3

I suggest you start by picking one point and drawing lines to 7 other points, then move onto the next point and do the same excluding the previous point since line has already been drawn. If you apply this method, first point will be matched with 7 points, and the next with 6 points, then 5, then 4, then 3, then 2, then 1.

That is, you have drawn: 7 + 6 + 5 + 4 + 3 + 2 + 1 = (8)(7)/2 = 28 lines

Now subtract (or erase) the 8 sides since all you want are diagonals. You get 20 diagonals in total.

In general, the # of diagonals in N-gon = (n)(n-1)/2 - n

Answer 4

d = n(n-3)/2 , where d is the number of diagonals and n = number of sides of polygon.
Thus for an octagon there are 8(8-3)/2 = 20 distinct diagonals. So OV and VO are the same diagonal and should be listed only once.

So if the octagon is named clockwise strting with O,
OWXRVTQS you would have OX,OR, OV, OT, and OQ
Then move to W and get WR, WV, WT, WXand WS. Now move to X and get XV, XT, XQ, XS, and XO. Now move to R getting RT, RQ, RS, RO, RW. Thats your 20 diagonals. If you now move to V you will be repaeting diagonals already named.

Answer 5

Formula for counting the number of diagonals is n(n-3)/2
where n is the number of sides. To count the diagonals, count every line segment that connects 2 nonconsecutive vertices; to name the diagonals, name every line segment. Check out the following sites for explanations and diagrams on how to draw and count the diagonals.