How do you prove that the sum of the angles of a triangle is 180 degrees? Is there a proof? what is it?
level: secondary or higher
Cut two copies of triangle ABC out of paper. Place the original with A at
the top and AB, say, on the left; place the first of the copies upside down
on the left with its vertex B on the original's A and vice versa. Place
the second copy on the right with its C and A on the original's A and C.
Note that the properties of parallel lines (alternate interior angles are
equal) force the bases of the two copies to line up parallel to the
original's base BC. One sees the three angles about A forming a straight
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