The number of triangles you can draw from one vertex is always two less
than the number of sides in the figure.   

-----Original Message-----
From: Middle Level Mathematics Network [mailto:[log in to unmask]]
On Behalf Of CAROL MCNAIR
Sent: Thursday, March 11, 2010 3:53 PM
To: [log in to unmask]
Subject: Re: [MLMATHNET] I have a question

Thanks.  I understand the triangle correlation, I just don't understand
the -2.  Why mathematically does that phenomenon work?  With a triangle,
when you take away two sides, you essentially end up with one side, that
is why I wondered if it had to do with straight angles.

Carol McNair
Team Sequoia
Camels Hump Middle School
>>> "Martin, Rick"  03/11/10 3:47 PM >>>
Carol, If you take a polygon with 5 sides and divide it into triangles
by connect a vertex to the other non-adjacent vertices, you will get
only 3 triangles - no matter which way you do it.  Therefore you have 3
triangles, each with angles that add to 180.  If you take a polygon in
general (with n sides), the number of triangles you can construct in
this same manner you will end up with n-2 triangles.  With some
diagrams, this becomes much more clear for students.  By the way it
works for all polygons, not just regular polygons.
Rick Martin
Colchester Middle School

________________________________________
From: Middle Level Mathematics Network [[log in to unmask]] On
Behalf Of CAROL MCNAIR [[log in to unmask]]
Sent: Wednesday, March 10, 2010 9:29 AM
To: [log in to unmask]
Subject: [MLMATHNET] I have a question

I have been thinking about an question, and can't find the answer.  Is
there anyone who might know?  I am trying to determine WHY the formula
(n-2)(180) works for finding sum of interior angles of regular polygons.
Is it because 1 line is a straight line with 180 degrees, and then
adding additional lines add 180 degrees, hence a triangle with 3 sides
is (3-2)(180)?


Carol McNair
Team Sequoia
Camels Hump Middle School
This e-mail may contain information protected under the Family
Educational Rights and Privacy Act (FERPA).  If this e-mail contains
student information and you are not entitled to access such information
under FERPA, please notify the sender.  Federal regulations require that
you destroy this e-mail without reviewing it and you may not forward it
to anyone.


This e-mail may contain information protected under the Family
Educational Rights and Privacy Act (FERPA).  If this e-mail contains
student information and you are not entitled to access such information
under FERPA, please notify the sender.  Federal regulations require that
you destroy this e-mail without reviewing it and you may not forward it
to anyone.

______________________________________________________________
______________________________________________________________
This email may contain information protected under the Family 
Educational Rights and Privacy Act (FERPA) or the Health Insurance 
Portability and Accountability Act (HIPAA).  If this email contains 
confidential and/or privileged health or student information and you 
are not entitled to access such information under FERPA or HIPAA, 
federal regulations require that you destroy this email without 
reviewing it and you may not forward it to anyone.


--
This message has been scanned for viruses and
dangerous content by MailScanner, ClamAV and Bitdefender  and is
believed to be clean.