MMD#3: Triangle Angle Sum

In every triangle, the angle measures add up to 180 degrees. Why is that?
Want to know.

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Dear Want to know,
For starters, let's consider a demonstration based on paper folding.

1. Starting with a sheet of unlined paper, cut out a triangle ABC, making side AB about 5 inches in length.
2. Fold side AB on itself so that the crease passes through vertex C.  This crease, labeled CD, is perpendicular to side AB.
3. Position vertex C on top of point D and crease the paper to form EF. 
4. Repeat Step 2 to create perpendiculars to AB through points E and F.
5. Using all three creases, fold the three vertices of triangle ABC together so that they converge at point D.  Together, these three angles precisely cover a 180 degree angle GDH.  Therefore the sum of  the three angles is 180 degrees.
6. Repeat this entire process with several other triangles.
7. How would you summarize your findings?  
8. This demonstration, while meant to be persuasive, is not a proof.  If you'd like to see that, let me know. 

For additional resources and ideas, visit my website math-ed.com 

Copyright David A. Thomas 2010  All Rights Reserved