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.