Euclid's Five Postulates Video Lecture | Mathematics (Maths) Class 9

What is Euclidean Geometry?
The word Geometry is derived from,
Geo means Earth
Metron means measure
Geometry is a branch of mathematics concerned
with questions of shape, size, relative position
of figures and shapes.
Euclidean Geometry is the study of geometry
based on definitions, terms and the assumptions
of the mathematician Euclid (330 B.C.)
It is the Geometry of flat surfaces
Euclid's wrote 13 books called the Elements
and was the first comprehensive discussion
of geometry.
And is credited with developing the first
comprehensive deductive system of geometry.
Euclidean Geometry is the study of flat space.
Euclidean Geometry can also be called plane
Geometry which is the study of lines and shapes
on a flat surface.
Euclidean Geometry can be illustrated on flat
paper or a chalkboard.
On a flat surface all of the following will
be true.
the shortest distance between two points is
a straight line.
the angles in any triangle add to 180 degrees.
A perpendicular line intersects another line
at 90 degree angles.
Euclidean Geometry cannot describe all physical
space such as curved space.
Non-Euclidean Geometry describes curved space
Euclid’s 5 Postulates (Axioms)
It is possible to draw a straight line from
any point to any point
If you have a straight line it is possible
to extend in any direction to infinity
It is possible to draw a circle given any
center and a radius
All right angles are equal (congruent)
If you have two straight lines, and a third
line crossing them, and the sum of the interior
angle measure of the two lines is less than
two 90 degrees, then if you extend the lines,
they will eventually cross on that side.
These 5 postulates are the foundation of Euclidean
Geometry and they are all about points, lines,
and planes
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