Pythagoras Theorem | Class 8 Mathematics Notes

Proof of Pythagoras Theorem

The NCERT textbook provides a geometric proof of the Pythagoras Theorem using area comparison. Consider a right-angled triangle with sides a, b, and hypotenuse c. Construct squares on each of these sides. The proof involves showing that the area of the square on the hypotenuse (c²) is equal to the sum of the areas of the squares on the other two sides (a² + b²). One common method is to arrange four copies of the right triangle inside a square of side (a + b), leaving a smaller square of side c in the center. By calculating the area of the large square in two different ways—once as (a + b)² and once as the sum of the areas of the four triangles and the small square—equating these expressions leads to the conclusion that c² = a² + b². This visual and algebraic approach helps students grasp the theorem intuitively and logically.

📊 Diagram: The diagram shows a large square of side (a + b) containing four identical right triangles arranged so that their hypotenuses form a smaller square in the center with side c. The figure illustrates the calculation of areas to prove the theorem.

🧪 Activity: Activity involves drawing the arrangement of four right triangles inside the square and verifying the area relationships.

🔗 Connection: Leads to the next section which discusses applications and examples using the theorem.