Revision Notes for Class 8 Maths Chapter 9: The Baudhayana-Pythagoras Theorem

Condensed revision notes for Class 8 Maths Chapter 9: The Baudhayana-Pythagoras Theorem – Ganita Prakash. These Class 8 Mathematics Chapter 9 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• Baudhayana-Pythagoras theorem: in a right triangle, (hypotenuse)² = (leg 1)² + (leg 2)².
• Indian origin: Baudhayana recorded this relationship in the Sulba Sutras, used for altar construction, centuries before Pythagoras in Greece.
• Isosceles right triangle: hypotenuse = side × √2.
• Doubling/halving a square: cutting along the diagonal and rearranging the resulting triangles relates areas by a factor of 2 — the basis of the theorem’s classic paper-folding proof.
• Baudhayana (Pythagorean) triple: three positive integers (a,b,c) with a²+b²=c².
• Primitive triple: HCF(a,b,c) = 1; e.g. (3,4,5), (5,12,13), (8,15,17).
• Non-primitive triple: a whole-number multiple of a primitive triple, e.g. (6,8,10) = 2×(3,4,5).
• Odd-square generation method: for odd n ≥ 3, the triple (n, (n²−1)/2, (n²+1)/2) is always a primitive Baudhayana triple.
• Hypotenuse is always the longest side of a right triangle.
• Lattice-grid square rule: a square of area x can be drawn on a dot grid exactly when x = p²+q² for integers p, q.
• Applications: finding missing sides of right triangles; diagonals of squares, rectangles and rhombi (via half-diagonals); area of an equilateral triangle via its altitude.
• Fermat’s Last Theorem (mentioned narratively in the chapter): no positive integer solutions exist for aⁿ+bⁿ=cⁿ when n > 2 — conjectured for centuries, proven true only in 1994.

More on this chapter: Solutions | Extra Questions | Class 8 Maths Book | Formulas Handbook

Frequently Asked Questions

What does the Pythagoras theorem, credited in ancient India to Baudhayana, state about a right triangle?
The theorem states that in a right-angled triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, a relationship also described earlier in the Baudhayana Sulba Sutra.

How is the Pythagoras theorem used to check whether a triangle is right-angled?
If the square of the longest side of a triangle equals the sum of the squares of the other two sides, the triangle must be right-angled, and this converse of the theorem is a practical way to verify a right angle without measuring it directly.

Written by Satish

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