1. Euclid’s Definitions 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

2. are basic facts which are obvious
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.

3. EUCLID’S AXIOMS EUCLID’ S GEOMETRY
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

4. EUCLID’S INCIDENCE AXIOMS
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.

5. EUCLID’S POSTULATES EUCLID’ S GEOMETRY
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.

6. EUCLID’ S GEOMETRY
Let’s Practice

7. EUCLID’ S GEOMETRY

8. EUCLID’ S GEOMETRY
Answer-1

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10. EUCLID’ S GEOMETRY
Answer-2

11. EUCLID’ S GEOMETRY
Answer-2 contd…..

12. EUCLID’ S GEOMETRY
Answer-3

13. EUCLID’ S GEOMETRY
Answer-4

14. EUCLID’ S GEOMETRY
Answer-5

15. EUCLID’ S GEOMETRY
Answer-5 contd….

16. EUCLID’ S GEOMETRY
Answer- 6

17. EUCLID’ S GEOMETRY
Answer- 7

18. EUCLID’ S GEOMETRY

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20. EUCLID’ S GEOMETRY
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