Portal:Euclidean geometry/Chapter 6

The Postulate

The sum of the lengths of two sides of a triangle is greater than the length of the third side.

Why it Matters

The sum of the angles of a triangle always equals 180 degrees. This is one of the most fundamental postulates with regard to triangles, and it is a derivative of this postulate.

Why the Postulate Works

Example One

Consider a triangle with side lengths 4, 4, and 8. This triangle would disprove the postulate, except that if you were to try to draw this triangle out, you would draw the longest side shorter than it should be, or, alternatively, you would end up with a mere line (not a triangle).

Example Two

Next, consider a triangle with side lengths 4, 4, and 16. This triangle would disprove the postulate, except that this "triangle" isn't even a polygon. If you were to try to draw it out, it either wouldn't be a closed figure or would only be a line.