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Before we try to prove this you should do an experiment to convince yourself that it is probably true.
| 1. | Take a piece of paper and cut out a triangle from it. |
| 2. | Label each angle with a letter. |
| 3. | Tear, not cut, each of the angles off. |
| 4. | Rearrange them to get a straight line, which we know is 180° |
We can make this completely logical. In Geometry we sometimes need to draw extra lines to help us see what is happening. These “constructions” are designed to help. Without them, there seems to be no way to go on. With them, the answer almost jumps out at us. The problem with cutting bits of paper is that, while it can show what we want for one triangle, it cannot prove our theorem for ALL triangles. If you examine the following proof, I hope you will agree that by drawing one extra line everything becomes clear:
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