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Class 8 The Baudhayana–Pythagoras Theorem: cheat sheet
CBSE Mathematics. In a right-angled triangle the square on the longest side equals the sum of the squares on the other two. The converse tests for a right angle.
Key ideas
- The hypotenuse is opposite the right angle and is the longest side.
- Baudhayana stated the result in the Sulba Sutras, long before Pythagoras.
- If the sides satisfy a² + b² = c² (c longest), the triangle has a right angle opposite c.
- Pythagorean triples are whole-number solutions: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25. Multiples of a triple are triples too.
- For a ladder against a wall, the ladder is the hypotenuse and the wall and ground are the other sides.
Remember
| Theorem | a² + b² = c² |
| Missing side | c = √(a² + b²); a = √(c² − b²) |
| Diagonal of a rectangle | d = √(l² + b²) |
| Making triples | 2m, m² − 1, m² + 1 (m > 1) |
Watch out
- Adding the squares when the hypotenuse is given and a shorter side is missing (subtract instead).
- Checking a² + b² = c² with c not the longest side.
- Forgetting to take the square root at the end.
Worked example
Check whether 45 cm, 30 cm and 53 cm can be the sides of a right-angled triangle.
Working: 30² + 45² = 2925; 53² = 2809
Answer: No
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