This document discusses the basic proportionality theorem and its converse. It begins by defining the basic proportionality theorem, also known as Thales' theorem, which states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides in the same ratio. It then provides a proof of this theorem. The document also discusses the history of Thales and the converse of the basic proportionality theorem. In the end, it discusses how PowerPoint can be used to enhance presentations by organizing content, providing illustrations, and animating slides.

1. BASIC
PROPORTIONALITY
THEOREM
AND CONVERSE OF IT!!!!!!

2. What is basic
proportionality
theorem?
This theorem is also called Thales
theorem.
It states that,
“If a line is drawn parallel to one
side of a triangle intersecting other
two sides, then it divides the two
sides in the same ratio.”

3. PROOF OF THALE’S
THEOREM
Given : In ∆ABC , DE || BC and intersects AB in D and AC in E.
To Prove : AD / DB = AE / EC
Construction : Join BC,CD and draw EF ┴ BA and DG ┴ CA
Proof:Statements Reasons
1) EF ┴ BA 1) Construction
2) EF is the height of ∆ADE and ∆DBE 2) Definition of perpendicular
3)Area(∆ADE) = (AD .EF)/2 3)Area = (Base .height)/2
4)Area(∆DBE) =(DB.EF)/2 4) Area = (Base .height)/2
5)(Area(∆ADE))/(Area(∆DBE)) = AD/DB 5) Divide (4) by (5)
6) (Area(∆ADE))/(Area(∆DEC)) = AE/EC 6) Same as above
7) ∆DBE ~∆DEC
7) Both the ∆s are on the same base and
between the same || lines.
8) Area(∆DBE)=area(∆DEC)
8) If the two triangles are similar their
areas are equal
9) AD/DB =AE/EC 9) From (5) and (6) and (7)

4. History of Thales
The ancient Greek philosopher Thales was born in Miletus in Greek Ionia. Aristotle, the major
source for Thales's philosophy and science, identified Thales as the first person to investigate the
basic principles, the question of the originating substances of matter and, therefore, as the
founder of the school of natural philosophy. Thales was interested in almost everything,
investigating almost all areas of knowledge, philosophy, history, science, mathematics,
engineering, geography, and politics. He proposed theories to explain many of the events of
nature, the primary substance, the support of the earth, and the cause of change. Thales was
much involved in the problems of astronomy and provided a number of explanations of
cosmological events which traditionally involved supernatural entities. His questioning approach
to the understanding of heavenly phenomena was the beginning of Greek astronomy. Thales'
hypotheses were new and bold, and in freeing phenomena from godly intervention, he paved
the way towards scientific endeavor. He founded the Milesian school of natural philosophy,
developed the scientific method, and initiated the first western enlightenment. A number of
anecdotes is closely connected to Thales' investigations of the cosmos. When considered in
association with his hypotheses they take on added meaning and are most enlightening. Thales
was highly esteemed in ancient times, and a letter cited by Diogenes Laertius, and purporting to
be from Anaximenes to Pythagoras, advised that all our discourse should begin with a reference
to Thales (D.L. II.4).

5. CONVERSE!!
•STATEMENT : If a line divides any two
sides of the triangle in the same
ratio, then the line is parallel to the
third side.

6. • Given : A Δ ABC and a line intersecting AB in D and AC in E,
such that AD / DB = AE / EC.
Prove that : DE || BC
• Proof:
Statements Reasons
1) DF || BC 1) By assumption
2) AD / DB = AF / FC 2) By Basic Proportionality theorem
3) AD / DB = AE /EC 3) Given
4) AF / FC = AE / EC 4) By transitivity (from 2 and 3)
5) (AF/FC) + 1 = (AE/EC) + 1 5) Adding 1 to both side
6) (AF + FC )/FC = (AE + EC)/EC 6) By simplifying
7) AC /FC = AC / EC 7) AC = AF + FC and AC = AE + EC
8) FC = EC
8) As the numerator are same so
denominators are equal
Hence DE II BC

7. H O W D O E S P O W E R P O I N T
P R E S E N T AT I O N E N H A N C E S
O U R P R O J E C T ? ? ? ? ?
I T E N H A N C E S O U R P R O J E C T B Y :
P O W E R P O I N T C A N B E U S E D T O :
1 : O R G A N I Z E A N D S T R U C T U R E Y O U R P R E S E N T A T I O N ;
C R E A T E A P R O F E S S I O N A L A N D C O N S I S T E N T F O R M A T ;
2 : P R O V I D E A N I L L U S T R A T I V E B A C K D R O P F O R T H E
C O N T E N T O F Y O U R P R E S E N T A T I O N ;
3 : A N I M A T E Y O U R S L I D E S T O G I V E T H E M G R E A T E R
V I S U A L I M P A C T .

8. F E AT U R E S O F P O E R P O I N T
P R E S E N T AT I O N U S E D .
T H E M A I N F E A T U R E S U S E D A R E :
1 . U S E O F A N I M A T I O N S .
2 . U S E O F D I F F E R E N T D E S I G N S O F S L I D E S .
3 . C U S T O M M A D E A N I M A T I O N I N S L I D E 3 A N D 1 0 .
4 . U S E O F D I F F E R E N T F O N T S .
5 . U S E O F D I F F E R E N T A T T R I B U T E S .
6 . M A K I N G O F T A B L E S .
7 . U S E O F Q U I C K S T Y L E S .
8 . U S E O F B U L L E T S .
9 . U S E O F S L I D E M A S T E R .
1 0 . U S E O F S M A R T A R T S .
1 1 . U S E O F T H E S A U R U S A N D S P E L L I N G S .
1 2 . U S E O F W O R D A R T S .

9. CREDITS
AKSHAT RAAHUL
JAYESH JADHAV

10. THANK YOU