The word ‘Geometry’ comes from Greek words ‘geo’ meaning the ‘earth’ and ‘metrein’ meaning to ‘measure’. Geometry appears to have originated from the need for measuring land. Nearly 5000 years ago geometry originated in Egypt as an art of earth measurement. Egyptian geometry was the statements of results. The knowledge of geometry passed from Egyptians to the Greeks and many Greek mathematicians worked on geometry. The Greeks developed geometry in a systematic manner..

2. INTRODUCTION TO
EUCLID'S GEOMETRY

3. TABLE OF CONTENT
 Introduction
 Euclid’s Definition
 Euclid’s Axioms
 Euclid’s Five Postulates
Theorems with Proof

4. INTRODUCTION
 The word ‘Geometry’ comes from
Greek words ‘geo’ meaning the
‘earth’ and ‘metrein’ meaning to
‘measure’. Geometry appears to
have originated from the need for
measuring land.
 Nearly 5000 years ago
geometry originated in Egypt as
an art of earth measurement.
Egyptian geometry was the
statements of results.
 The knowledge of geometry

5.  Euclid was the first Greek
Mathematician who initiated a new way
of thinking the study of geometry
 He introduced the method of proving a
geometrical result by deductive
reasoning based upon previously proved
result and some self evident specific
assumptions called AXIOMS
 The geometry of plane figure is known
as ‘Euclidean Geometry’. euclid is known
as the father of geometry.

6. EUCLID’S DEFINITONS
Some of the definitions made by
Euclid in volume I of ‘the
elements’ that we take for
granted today are as follows :-
A point is that which has no part
A line is breadth less length
The ends of a line are points
A straight line is that which has
length only

7. Continued…..
The edges of a surface are lines
A plane surface is a surface which
lies evenly with the straight lines
on itself
Axioms or postulates are the
assumptions which are obvious
universal truths. They are not
proved.
Theorems are statements which
are proved, using definitions,

8. EUCLID’S AXIOMs
some of euclid’s axioms were :-
Things which are equal to the same
thing are equal to one another.
i.e. if a=c and b=c then a=b.
Here a,b, and c are same kind of
things.
 If equals are added to equals, the
wholes are equal.

9. Continued…..
i.e. if a=b and c=d, then a+c = b+d
Also a=b then this implies that
a+c=b+c.
If equals are subtracted, the
remainders are equal.
Things which coincide with one
another are equal to one another.

10. Continued…..
The whole is greater than the
part.
That is if a > b then there exists c
such that a =b + c. Here, b is a part
of a and therefore, a is greater
than b.
Things which are double of the
same things are equal to one

11. EUCLID’S FIVE POSTULATES
euclid’s postulates were :-
POSTULATE 1:-
 A straight line may be drawn from
any one point to any other point
Axiom :-
 Given two distinct points, there is a
unique line that passes through
them

12. Continued…..
 POSTULATE 2 :-
A terminated line can be produced
infinitely
POSTULATE 3 :-
 A circle can be drawn with any centre
and any radius
POSTULATE 4 :-
 All right angles are equal to one
another

13. Continued…..
POSTULATE 5 :-
 If a straight line falling on two
straight lines makes the interior
angles on the same side of it taken
together less than two right
angles, then the two straight
lines, if produced indefinitely, meet
on that side on which the sum of
angles is less than two right

14. Example :-
 In fig :- 01 the line EF falls on two
lines AB and CD such that the angle
m + angle n < 180° on the right side
of EF, then the line eventually
intersect on the right side of EF
fig :-
o1

15. CONTINUED…..
THEOREM
 Two distinct lines cannot have
more than one point in common
 PROOF
two lines ‘l’ and ‘m’ are given. we
need to prove that they have only
one point in common
Let us suppose that the two lines
intersects in two distinct points, say
P and Q

16.  That is two line passes through two
distinct points P and Q
 But this assumptions clashes with the
axiom that only one line can pass
through two distinct points
 Therefore the assumption that two
lines intersect in two distinct points is
wrong
 Therefore we conclude that two
distinct lines cannot have more than one
point in common