write Euclid's fifth postulate in two different way.
Answers
Answered by
5
Besides 23 definitions and several implicit assumptions, Euclid derived much of the planar geometry from five postulates.
A straight line may be drawn between any two points.
A piece of straight line may be extended indefinitely.
A circle may be drawn with any given radius and an arbitrary center.
All right angles are equal.
If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
The fifth postulate refers to the diagram on the right. If the sum of two angles A and B formed by a line L and another two lines L1 and L2 sum up to less than two right angles then lines L1 and L2 meet on the side of angles A and B if continued indefinitely.
Postulates 1 and 3 set up the "ruler and compass" framework that was a standard for geometric constructions until the middle of the 19th century. They may be said to be based on man's practical experience. The second postulate gives an expression to a commonly held belief that straight lines may not terminate and that the space is unbounded. By the Definition 10, an angle is right if it equals its adjacent angle. Thus the fourth postulate asserts homogeneity of the plane: in whatever directions and through whatever point two perpendicular lines are drawn, the angle they form is one and the same and is called right. We may think of the fourth postulate as having been justified by the everyday experience acquired by man in the finite, inhabited portion of the universe which is our world and extrapolated (much as the Postulate 2) to that part of the world whose existence (and infinite expense) we sense and believe in.
A straight line may be drawn between any two points.
A piece of straight line may be extended indefinitely.
A circle may be drawn with any given radius and an arbitrary center.
All right angles are equal.
If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
The fifth postulate refers to the diagram on the right. If the sum of two angles A and B formed by a line L and another two lines L1 and L2 sum up to less than two right angles then lines L1 and L2 meet on the side of angles A and B if continued indefinitely.
Postulates 1 and 3 set up the "ruler and compass" framework that was a standard for geometric constructions until the middle of the 19th century. They may be said to be based on man's practical experience. The second postulate gives an expression to a commonly held belief that straight lines may not terminate and that the space is unbounded. By the Definition 10, an angle is right if it equals its adjacent angle. Thus the fourth postulate asserts homogeneity of the plane: in whatever directions and through whatever point two perpendicular lines are drawn, the angle they form is one and the same and is called right. We may think of the fourth postulate as having been justified by the everyday experience acquired by man in the finite, inhabited portion of the universe which is our world and extrapolated (much as the Postulate 2) to that part of the world whose existence (and infinite expense) we sense and believe in.
NarwalVarsha:
Alplali have u copied from Google
Answered by
6
●If A Straight line is falling on two straight lines to make the interior angles on the same side if it is taken together less than the 2 right angles, then it will produce incorrectly so meet on that side on which the sum of angles is less than two right angles.
● Teo distinct intersecting lines cannot be parallel.
HOPE IT HELPS YOU.
● Teo distinct intersecting lines cannot be parallel.
HOPE IT HELPS YOU.
Welcome all
Similar questions