Chapter 9 — The Baudhayana-Pythagoras Theorem

Chapter 9 of Class 8 maths, "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.

This chapter explores the ancient Baudhayana theorem, credited to the 8th-century sage Baudhāyana and later studied by Pythagoras. Students learn how to construct squares with specific area relationships, understand isosceles right triangles and their hypotenuses, and master the theorem a² + b² = c² for right-angled triangles. The chapter covers Baudhayana triples (integer solutions like 3-4-5), irrational numbers such as √2, and applications in solving geometric problems, culminating in Fermat's Last Theorem.

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