Making Triangles

Date: 11/12/2001 at 14:29:56
From: David
Subject: Demonstrating triangles

I've been trying to find ways to demonstrate a triangle that contains 
180 degrees without using a protractor.

-Dave

Date: 11/12/2001 at 15:50:27
From: Doctor Peterson
Subject: Re: Demonstrating triangles

Hi, David.

Here's a simple way to demonstrate what you want. Three angles that 
add up to 180 degrees can be put together to form a straight angle (a 
line):

       \     /
        \   /
        a\b/c
    ------+------

So make a triangle out of paper, tear off the three corners, and fit 
them together this way. They should always form a straight line.

Or, to make a more impressive demonstration that comes close to a 
geometrical proof, place your triangle so that angles a and c are both 
acute (b may be obtuse), and fold the corners in (dividing two edges 
in half) so they all meet on the remaining edge:

              +
             / b \
            /       \
           /           \
          /     fold      \
         +-------------------+
        /|f                 f|  \
       / |o                 o|     \
      /  |l                 l|        \
     /a  |d                 d|         c \
    +----+-------------------+--------------+

         +-------------------+
         |\               /  |
         | \           /     |
         |  \       /        |
         |  a\ b /c          |
         +----+--------------+

You will end up with a rectangle surrounding three angles that 
together form its bottom edge: 180 degrees.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/