Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In absolute geometry, the Saccheri–Legendre theorem asserts that the sum of the angles in a triangle is at most 180° in any geometry satisfying the first four Euclidean postulates. The theorem is named after Giovanni Girolamo Saccheri and Adrien-Marie Legendre. From this theorem, the existence of triangle with angle sum of 180 degrees implies the Euclid's parallel postulate. Similarly, the existence of at least 1 triangle with angle sum of less than 180 degrees imply the Hyperbolic geometry.

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