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Introduction to Euclid’s Geometry

Jan 09, 2016

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Rishabh Sardana

Geometry lesson for primary schools
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    Rishabh, IX A , Roll no, - 36

    KB DAV Senior Secondary

    Public School

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    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.

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    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.

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    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.

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    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.

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    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$

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    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

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    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$

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    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

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    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$

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