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### 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/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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