7/17/2019 Introduction to Euclids Geometry
1/11
Rishabh, IX A , Roll no, - 36
KB DAV Senior Secondary
Public School
7/17/2019 Introduction to Euclids Geometry
2/11
PostulatesPostulates
1.1. A straight line may be drawn fromA straight line may be drawn from
any one point to any other point.any one point to any other point.
2.2. A terminated line can be producedA terminated line can be produced
indefinitely.indefinitely.
3.3. A circle can be drawn with anyA circle can be drawn with any
centre and any radius.centre and any radius.
7/17/2019 Introduction to Euclids Geometry
3/11
PostulatesPostulates
4.4. All right angles are equal to one another.All right angles are equal to one another.
5.5. If a straight line falling on two straightIf a straight line falling on two straight
lines makes the interior angles on thelines makes the interior angles on thesame side of it taken together less thansame side of it taken together less than
two right angles then the two straighttwo right angles then the two straight
lines if produced indefinitely meet onlines if produced indefinitely meet on
that side on which the sum of angles isthat side on which the sum of angles isless than two right angles.less than two right angles.
7/17/2019 Introduction to Euclids Geometry
4/11
Aio!sAio!s
1.1. !hings which are equal to the same!hings which are equal to the same
thing are equal to one another.thing are equal to one another.
2.2. If equals are added to equals theIf equals are added to equals the
wholes are equal.wholes are equal.
3.3. If equals are subtracted fromIf equals are subtracted from
equals the remainders are equal.equals the remainders are equal.
7/17/2019 Introduction to Euclids Geometry
5/11
Aio!sAio!s
4.4. !hings which coincide with one!hings which coincide with one
another are equal to one another.another are equal to one another.
5.5. !he whole is greater than the part.!he whole is greater than the part.
".". !hings which are double of the same!hings which are double of the same
things are equal to one another.things are equal to one another.
#.#. !hings which are hal$es of the same!hings which are hal$es of the same
things are equal to one another.things are equal to one another.
7/17/2019 Introduction to Euclids Geometry
6/11
So!e De"initions
#$ Point % A s!all dot !ade by a
shar& &encil on a sheet o" &a&er
'i(es an idea about a &oint$ A
&oint has no di!ension$ It hasonly a &osition$
)$ *ine % It should be a strai'ht line
and etended inde"initely to both
the directions$
7/17/2019 Introduction to Euclids Geometry
7/11
So!e De"initions
3$ Plane % Sur"ace o" a s!ooth+all, sur"ace o" a sheet o" &a&erare called &lane$ Sur"ace is that
+hich has len'th and breadthonly$
$ Ray % A &art o" the line * +hich
has only one end A and containsthe &oint B, then AB is a ray$
A BL
7/17/2019 Introduction to Euclids Geometry
8/11
So!e De"initions
$ An'le% .hen t+o linesdi(er'e "ro! a co!!on&oint, an an'le is "or!ed$
6$ /ircle % It is a set o" all those&oints in a &lane +hosedistance "ro! a "ied &oint
re!ains constant$ 0he "ied&oint is called the centre o"the circle$
7/17/2019 Introduction to Euclids Geometry
9/11
So!e De"initions
1$ *ine se'!ent % A linese'!ent is a &art o" line+hen t+o distinct &oints, let
A and B on a line are 'i(en$0hen the &art o" this line +ithend &oints A and B is called aline se'!ent$
2$ Radius % 0he distance "ro!the center to a &oint on thecircle is called the radius o"the circle$
A B
r
7/17/2019 Introduction to Euclids Geometry
10/11
So!e De"initions
$ S4uare % A 4uadrilateral in
+hich all the "our an'les are
ri'ht an'les and all the "our
sides are e4ual$
7/17/2019 Introduction to Euclids Geometry
11/11