Chapter 9 — The Baudhayana-Pythagoras Theorem

Chapter 9 of the Class 8 Maths NCERT textbook (Ganita Prakash), "The Baudhayana-Pythagoras Theorem", teaches the fundamental relationship between the sides of a right-angled triangle, where the square of the hypotenuse equals the sum of squares of the other two sides (a² + b² = c²), along with applications in geometry and number theory.

• The right-triangle relationship — Building from areas of squares on a triangle's sides, the chapter establishes that for any right triangle the squares on the two legs together equal the square on the hypotenuse, and applies it to solve geometric problems.
• Integer solutions and irrationals — Students meet Baudhayana triples — whole-number side sets like 3-4-5 — and how primitive triples scale to all others, while the isosceles right triangle surfaces the irrational number √2.
• History and a famous frontier — Credited to the sage Baudhayana and later to Pythagoras, the theorem is placed in its ancient context and pushed to its modern edge in Fermat's Last Theorem, which fails for powers above two.

1. 01The square constructed on the diagonal of a square has double the area of the original square
2. 02For a right-angled triangle with sides a, b and hypotenuse c: a² + b² = c²
3. 03The hypotenuse of an isosceles right triangle with equal sides of length a is c = a√2
4. 04√2 is approximately 1.41421356 and cannot be expressed as a terminating decimal or fraction
5. 05Baudhayana triples are sets of three positive integers (a, b, c) satisfying a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17)
6. 06Primitive Baudhayana triples have no common factor greater than 1, and all triples can be generated by scaling primitive ones
7. 07Fermat's Last Theorem (proved by Andrew Wiles in 1994) states that xⁿ + yⁿ = zⁿ has no solution for n > 2