EUCLID’ S GEOMETRY

• A point has no part or dimension. • A line has no breadth.• Ends of a line are points.• A straight line is a line which lies evenly with the

points on itself.• A surface has length and breadth only.• Edges of a surface are lines.• A plane surface is a surface which lies evenly with the

straight lines on itself.

Euclid’s Definitions

EUCLID’ S GEOMETRY

Axioms or Postulates-

• are basic facts which are obvious

• universal truths. They are not proved.

Theorems-

• are statements which are proved , using definitions, axioms, previously proved statements and deducting reasoning.

• Are axioms related to geometry.

EUCLID’ S GEOMETRY

EUCLID’S

AXIOMS

• Things that are equal to the same thing are equal to each other. If, a=b and b=c then a=c

• If equals are added to equals then wholes are equal. If a=b then a+c = b+c

• If equals are subtracted from equals then remainders are equals. If a=b then a-c = b-c

• Things which coincide with each other are equal to one another.

• The whole is greater than the part.• Things which are double or halves of the same thing

are equal. If a = b then 2a= 2b and (a/2) = (b/2)

• If first thing is greater than the secon and second is greater than the third , then first is greater than the third. If a>b>c then a>c

EUCLID’ S GEOMETRY

EUCLID’S INCIDENCE

AXIOMS

• A line contains infinitely many points.• Through a given point there pass

infinitely many lines.• Given two points A and B, there is one

and only one line that contains both the points.

• Things which are double of same things are equal to one another.

• Things which are halves of the same things are equal to one another.

EUCLID’ S GEOMETRY

EUCLID’S

POSTULAT

ES

• A straight line may be drawn from any one point to another point.

• A terminated line may be produced indefinitely.

• A circle can be drawn with any center and any radius.

• All right angles are equal to one another• 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, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

EUCLID’ S GEOMETRY

Let’s Practice

EUCLID’ S GEOMETRY

EUCLID’ S GEOMETRY

Answer-1

EUCLID’ S GEOMETRY

EUCLID’ S GEOMETRY

Answer-2

EUCLID’ S GEOMETRY

Answer-2 contd…..

EUCLID’ S GEOMETRY

Answer-3

EUCLID’ S GEOMETRY

Answer-4

EUCLID’ S GEOMETRY

Answer-5

EUCLID’ S GEOMETRY

Answer-5 contd….

EUCLID’ S GEOMETRY

Answer- 6

EUCLID’ S GEOMETRY

Answer- 7

EUCLID’ S GEOMETRY

EUCLID’ S GEOMETRY

EUCLID’ S GEOMETRY

THANK YOU