Presentation on Euclid's Geometry for class 9.

1. Presentation on
Euclid’s Geometry
By Kavyaa Ghosh
Class IX-A
19

2. Contents of the Presentation
i. What is Geometry?
ii. Who is Euclid?
iii. What is Axiom?
iv. Euclid’s Axioms
v. What is Postulate?
vi. Euclid’s Postulates
vii. Fifth Postulate of Euclid
viii. Theorems

3. What is Geometry?
• The branch of mathematics concerned with the properties and relations of
points, lines, surfaces, solids, and higher dimensional analogues.
• Geometry is one of the oldest branches of Mathematics, along with
arithmetic.
• ‘Geometry’ is derived from two Greek words:- Geo which means Earth and
Metron which means measure.

4. Who is Euclid?
• Euclid was a Greek mathematician, also known as ‘Father of Geometry’, was
also an active geometer and logician.
• Euclid is generally considered among the greatest mathematicians of
antiquity, and one of the most influential in the history of mathematics.
• Euclid was a teacher at Alexandria in Egypt who collected all the known
work and arranged it in his famous treatise, called ‘Elements’.
• A treatise means a written work dealing formally and systematically with a
subject.

5. What is Axiom?
• An axiom or assumption is a statement that is taken to be true.
• Axioms are the common notions which can be used throughout mathematics
and are not specifically linked or limited to geometry.
• Axios
• Worthy
Greek
• Axioma
• What is
thought
fitting
Greek
• Axioma
• Axiome
Latin
French Axiom

6. Euclid’s Axioms
• Things which are equal to the same thing are equal to one another.
• If equals are added to equals, the wholes are equal.
• If equals are subtracted from equals, the remainders are equal.
• Things which coincide with one another are equal to one another
• The whole is greater than the part.
• Things which are double of the same things are equal to one another
• Things which are halves of the same things are equal to one another

7. What is Postulate?
• Postulates is the term used by Euclid for the assumptions which are specified
to geometry only.
Latin • Postulare
Latin • Postulat- (asked)
English • Postulate (late middle
English)

8. Euclid’s Postulates
• A straight line may be drawn from any one point to any other point.
• A terminated line can be produced indefinitely.
• A circle can be drawn with any centre 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, then the two straight lines, if
produced indefinitely, meet on that side on which the sum of angles is less than two
right angles.

9. Fifth Postulate of Euclid
Euclid’s fifth postulate also has it’s own equivalent versions. Those versions
are:-
1. ‘For every line l and for every point P not lying on l, there exists a unique line m passing
through P and parallel to l’.
2. Two distinct intersecting lines cannot be parallel to the same line.

10. Theorems
• Theorems are statements which are proved, using definitions, axioms,
previously proved statements and deductive reasoning.
Greek
• Theoros
• (Spectator)
Greek
• Theorein
• (Look at)
Greek
• Theorema
• (Speculation)
French
• Theoreme
English
• Theorem
• Mid 16th
Century

11. Thank You
Have a Nice Day
- Kavyaa Ghosh
- Class IX-A
- 9019