How can you prove that the angles of a triangle add upto 180 degrees?
There are a bunch of proofs, but I think the coolest one involves simple copying of the triangle. First, take a random triangle and label the angles a, b, and c. Next, extend the “bottom” of the triangle in both directions. “Copy” the triangle (a congruent one) to the left of the first one. Now, connect the two points on the triangles that are not on the line. You’ll get a third, upside down triangle. You can show that these three triangles are congruent, and that the point where all three of them meet on the line has angles a,b, and c. Therefore, a+b+c = a straight line = 180 degrees.
