However, in the past two centuries, assorted non-Euclidean geometries have been derived based on using the first four Euclidean postulates together with various negations of the fifth. As a result, many mathematicians over the centuries have tried to prove the results of the Elements without using the Parallel Postulate, but to no avail. Mathematicians, and really most of us, value simplicity arising from simplicity, with the long complicated proofs, equations, and calculations needed for rigorous certainty done behind the scenes, and to have such a long sentence amidst such other straightforward, intuitive statements seems awkward. Postulate 5, the so-called Parallel Postulate was the source of much annoyance, probably even to Euclid, as it is not a simple, concise statement, as are the other four. Postulate 4: All the right angles are similar to one another. Postulate 3: The circle can be drawn with any centre and radius. Postulate 2: A terminated line can be produced indefinitely. Determine whether you can use the cases SAS, SSS, ASA postulates or ASA theorem to prove. Ans: Euclid’s five postulates are given below: Postulate 1: A straight line can be drawn from any point to any other point. (b) The altitude to the hypotenuse of a right triang. If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles. Prove each statement (in Euclidean geometry): (a) The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to each other and to the original triangle.A circle may be described with any given point as its center and any distance as its radius. Euclids Geometry was introduced by the Greek mathematician Euclid, where Euclid defined a basic set of rules and theorems for a proper study of geometry.

A straight line may be extended to any finite length.A straight line segment may be drawn from any given point to any other.Together with the five axioms (or 'common notions') and twenty-three definitions at the beginning of Euclid's Elements, they form the basis for the extensive proofs given in this masterful compilation of ancient Greek geometric knowledge. The five postulates of Euclidean Geometry define the basic rules governing the creation and extension of geometric figures with ruler and compass. Postulates in geometry is very similar to axioms, self-evident truths, and beliefs in logic, political philosophy, and personal decision-making.

Basic postulate of euclidean geometry