Question 623954: how does the fact that the angles of a triangle add up to 180 degrees depend on the validity of the parallel postulate? Answer by solver91311(24713) (Show Source):
Construct a triangle with the bottom side horizontal. Construct a line parallel to the horizontal side through the vertex at the top of the triangle.
You have just formed three angles. The one in the middle is one of the interior angles of the triangle. Because of the equality of opposite interior angles of a transversal which follows from the parallel postulate, the other two angles are equal to the angles at the base of triangle. So you have three angles that form a straight angle which by definition measures 180 degrees equal to the three angles of an arbitrary triangle. QED.
John
My calculator said it, I believe it, that settles it
