Triangle Postulate

In Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate. The following statements are equivalent:

  • Triangle postulate: The sum of the angles of a triangle is two right angles.
  • Playfair's axiom: Given a straight line and a point not on the line, exactly one straight line may be drawn through the point parallel to the given line.
  • Proclus' axiom: If a line intersects one of two parallel lines, it must intersect the other also.
  • Equidistance postulate: Parallel lines are everywhere equidistant.
  • Triangle area property: The area of a triangle can be as large as we please.
  • Three points property: Three points either lie on a line or lie on a triangle.
  • Pythagoras' theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Other articles related to "triangles, triangle":

Triangle Inequality - Euclidean Geometry - Right Triangle
... A specialization of this argument to right triangles is In a right triangle, the hypotenuse is greater than either of the two sides, and less than their ... is established above for any side of any triangle ... In the figure, consider the right triangle ADC ...