Geomtry Question?

Question

I had a packet of geometry problems and this is the only one I can't figure out. Please HELP! Good luck and thanks.

1. There is a pentagon with a star inside it touching all 5 corners of the pentagon. The star is drawn with the lines inside the star (5 lines inside). How many triangles are in the diagram?

Answer 1

Does the figure look like this?

http://www.jimloy.com/geometry/pentagon.htm

If so... then there are a total of 35 triangles...

Here's how you count them....

If you just count the small triangles that you see... there are 10.... PLUS...

5 that are similar to the green triangle at the bottom combined with the triangle with "a+b" written in it....

Plus another 5 that are similar to the triangle with "a+b" written in it combined with the small beige triangle to the right of it...

Plus 5 more that look like the combination of 3 triangles (the triangle with "a+b" written in it AND the small beige triangle to the right, PLUS the triangle with the "a" written in it...) Since the bigger pentagon has 5 angles... then there are 5 of these big triangles...

Plus 5 more bigger triangles that are a combination of the bottom green triangle, the small pentagon in the middle, PLUS the small triangle to the right of the top green triangle)... Since there are 5 angles in the middle smaller pentagon, there are 5 of these bigger triangles that I was describing...

Plus 5 more bigger triangles that are a combination of the two left small beige triangles, the bottom green triangle, the small pentagon in the middle, and the small beige triangle with the "b" written in it)... On of the side of this large triangle shares a side with the larger pentagon. Since the larger pentagon has 5 sides, the are 5 of these larger triangles that I was describing...

Altogether, there are 10 + 5 + 5 + 5 + 5 + 5 = 10 + 25 = 35 triangles in the diagram, when you count all the small triangles, plus the varioius larger triangles that are composed of the smaller triangles. That's how you get the 35 triangles...

Confused? Then check this link out...

http://www.ithaca.edu/dani/SeeLogo/Stars/activities.html

It illustrates by using colors what triangles I'm talking about...

In your pentagon/star figure, there are:

5 yellow triangles
5 red triangles
5 orange triangles
5 evergreen triangles
5 purple triangles
5 light green triangles, and
5 blue triangles....
--------------------------
for a GRAND TOTAL of 35 triangles...

Hope this helps!!!

I give you a star because this was a GREAT question you asked!!!

Answer 2

I don't remember enough about vertices and such to solve it mathematically, but there are many more than 10 triangles.

I get 28, although I've seen 35 for an answer. (Can't figure out where more are, if they exist.)

Start at the vertex at 12 o'clock. There are eight triangles touching that vertex: three on the left, two in the center and three on the right. (Don't count the left and right triangles in the middle; they don't touch the 12 o'clock vertex.)

Then at 2 o'clock, there are another eight triangles, but three of them have already been counted, leaving five. The same is true for the other three vertices, for a total of 28.

Answer 3

i got 30
but i would keep trying to figure it out
maybe cut out each peice and do like a puzzle
that should help
hope this helped
but it is more than 10 i can tell you that for sure
because from one side of the pentagon there is two lines going to the opposite side and that makes another triangle
so DONT USE 10! i can promise you that isnt the answer

Answer 4

this is both geometry and a bit of a brain teaser... the best way to solve it is to draw it. You have a pentagon with a pentagram inside of it. Start counting. Remember -- there are times when two or more smaller triangles make one larger triangle. You have to count those too!

Answer 5

well pentagon is 5 sided shape right? A star has 5 points I think?? So would there be 10 triangles?

I have no clue without seeing the diagram

sorry

Answer 6

This Site Might Help You.

RE:
Geomtry Question?
I had a packet of geometry problems and this is the only one I can't figure out. Please HELP! Good luck and thanks.

1. There is a pentagon with a star inside it touching all 5 corners of the pentagon. The star is drawn with the lines inside the star (5 lines inside). How many triangles are...

Answer 7

Since the ray bisects the angle, it cuts it into two equal peices. That means that ABD=DBC (or the other angle). You write the equations out like this (2x-y)=(3y-x) and solve it for the different variables. (x=4y/3) and (y=3x/4) maybe i'm just retarted...

Answer 8

Just draw what it tells you to and count the triangles. Pssst the answer is 10.

Answer 9

Count them

Answer 10

draw a pentagon and a star inside of it. count the triangles. it's cake, darlin'.