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A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "axioms" and five "postulates."

A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "[[axiom]]s" and five "postulates."

==The fifth postulate==

==Euclid's fifth postulate==

Most of Euclid's axioms and postulates do seem to be "true without needing proof;" for example, "Things which are equal to the same thing are also equal to one another."

Most of Euclid's axioms and postulates do seem to be "true without needing proof;" for example, "Things which are equal to the same thing are also equal to one another."

Euclid's fifth postulate, the ''parallel postulate,'' however, is a little different. It says:

Euclid's fifth postulate, the ''parallel postulate,'' however, is a little different. It says:

:It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.

:It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.

This is sometimes stated in an equivalent form:

This is sometimes stated in an equivalent form, known as Playfair's axiom:

:Given a line and a point not on that line exactly one line can be drawn through that point which does not intersect the original line.

:Given a line and a point not on that line exactly one line can be drawn through that point which does not intersect the original line.