The document explains the Pythagorean theorem, a key property of right-angled triangles stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides. It also provides a brief overview of Pythagoras, a Greek mathematician who is credited with proving this property, and highlights real-life applications such as navigation and measuring heights. Additionally, it mentions Pythagorean triplets, which are sets of three natural numbers that satisfy the theorem.

1. MATHEMATICS

2. WHAT IS PYTHAGORAS
THEOREM?
MATHEMATICS

3. PYTHAGORAS IS SAID TO HAVE FOUND THE VERY IMPORTANT
PROPERTY OF RIGHT ANGLED TRIANGLES, CALLED PYTHAGORAS
THEORUM.THE PROPERTY HAS BEEN NAMED AFTER HIM AS HE IS
BELIEVED TO HAVE BEEN THE FIRST TO GIVE A PROOF OF THIS
PROPERTY.
THE THEOREM STARTED AS:
IN A RIGHT ANGLED TRIANGLE, THE SQUAREOF THE
HYPOTENUSE IS EQUAL TO THE SUM OF THE SQUARES OF OTHER TWO
SIDES.
PYTHAGORAS THEOREM.

4. NOTE: PYTHAGORAS THEOREM HOLDS TRUE ONLY IF THE TRIANGLE
IS RIGHT ANGLED.
PYTHAGORAS THEOREM.
MATHEMATICS

5. WHO WAS PYTHAGORAS?
MATHEMATICS

6. PYTHAGORAS WAS A BRILLIANT GREEK MATHEMATICIAN AND
PHILOSOPHER OF 6th CENTURY BC.
PYTHAGORAS
MATHEMATICS

7. APPLICATION & USAGE OF
PYTHAGORAS THEOREM IN REAL LIFE.
IT IS THE STARTING PLACE FOR TRIGNOMETRY.
IT IS USED TO MEASURE THE UNKNOWN HEIGHTS OF OBJECTS.
IT IS USED IN NAVIGATION, CARTOGRAPHY, FINDING ANGLES
OF ELEVASION AND DEPRESSION.
MATHEMATICS

8. MATHEMATICS
REAL LIFE SITUATIONS WHERE WE USE
PYTHAGORAS THEOREM:

9. MATHEMATICS

10. MATHEMATICS

11. MATHEMATICS

12. MATHEMATICS
PROOF FOR PYTHAGORAS THEOREM

13. PYTHAGOREAN TRIPLET
THREE NATURAL NUMBERS IN WHICH THE SQUARE OF LARGEST
NUMBER IS EQUAL TO THE SUM OF THE SQUARE OF THE OTHER TWO
NUMBERS FORM A PYTHAGOREAN TRIPLET.
SOME PYTHAGOREAN TRIPLETS:
9,12,15
3,4,5
5,12,13
6,8,10
8,15,17
7,24,30
12,35,37
15,36,39
MATHEMATICS

14. THANK YOU
PRESENTED BY
M.AJITESH
VII B
MATHEMATICS