NCERT Class 8 Maths Chapter 9
The Baudhāyana-Pythagoras Theorem
NCERT Class 8 Maths Chapter 9 (Ganita Prakash Part 2) explores one of the most famous theorems in mathematics — the relationship between the sides of a right-angled triangle. This CBSE chapter honours the ancient Indian mathematician Baudhāyana, who stated this result before Pythagoras. Students learn to apply the theorem to find unknown sides, verify right angles, and solve real-world problems involving distances and heights.
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Key Terms
- Pythagoras Theorem
- In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².
- Hypotenuse
- The longest side of a right-angled triangle, always opposite the right angle (90°).
- Right-angled Triangle
- A triangle that has one interior angle exactly equal to 90°; the side opposite the right angle is the hypotenuse.
- Pythagorean Triplet
- A set of three positive integers (a, b, c) satisfying a²+b²=c², representing valid side lengths of a right-angled triangle; e.g., (3,4,5), (5,12,13).
- Converse of Pythagoras Theorem
- If c²= a²+b² in a triangle, then the triangle is right-angled (with the right angle opposite side c).
- Baudhāyana
- Ancient Indian mathematician (800–600 BCE) who stated the Pythagorean relationship in the Sulbasutras, predating Pythagoras by several centuries.
- Altitude
- A perpendicular line segment from a vertex of a triangle to the opposite side; in a right triangle, the altitude to the hypotenuse creates important proportional relationships.
Frequently Asked Questions
What is the Pythagoras theorem Class 8 Maths?▾
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: c² = a² + b². For example, if a = 3 and b = 4, then c² = 9 + 16 = 25, so c = 5. NCERT Class 8 Chapter 9 explores this theorem and its applications.
Who was Baudhāyana Class 8 NCERT?▾
Baudhāyana was an ancient Indian mathematician who lived around 800–600 BCE. He stated the relationship between the sides of a right-angled triangle in his Sulbasutras (ancient Indian texts on geometry used for constructing Vedic altars) centuries before the Greek mathematician Pythagoras stated it. NCERT Class 8 Chapter 9 acknowledges this Indian contribution to mathematics.
How do you use the Pythagoras theorem to find missing sides Class 8?▾
To find the hypotenuse: c = √(a²+b²). Example: legs = 6 and 8; hypotenuse = √(36+64) = √100 = 10. To find a leg: a = √(c²-b²). Example: hypotenuse = 13, one leg = 5; other leg = √(169-25) = √144 = 12. Always check which side is the hypotenuse (opposite right angle).
What are common Pythagorean triplets Class 8 Maths?▾
Common Pythagorean triplets to memorise: (3,4,5), (5,12,13), (8,15,17), (7,24,25), (6,8,10 — multiples of 3,4,5), (9,12,15). To generate new triplets using integer m > 1: sides are 2m, m²-1, m²+1. These triplets represent whole-number side lengths of right-angled triangles and are very useful in CBSE exam problems.
What is the converse of the Pythagoras theorem Class 8?▾
The converse states: if in a triangle with sides a, b, c (where c is the longest), c² = a² + b², then the triangle is right-angled. This lets us check whether a triangle is right-angled without measuring angles. Example: sides 5, 12, 13 — check: 5²+12² = 25+144 = 169 = 13² ✓ — so it is a right-angled triangle.
What are the real-life applications of the Pythagoras theorem Class 8?▾
Real-life applications: (1) Construction — checking if corners are at right angles (using a 3-4-5 rope), (2) Navigation — finding the shortest distance between two points, (3) Architecture — calculating diagonal lengths and heights, (4) Screen sizes — diagonal measurement of TVs and phones, (5) Surveying — measuring distances across rivers or fields. NCERT Class 8 Chapter 9 includes such practical problems.
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