Pythagoras Theorem
ICSE · Class 9 · Mathematics
Quick revision notes for Pythagoras Theorem — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Statement and Basic Understanding
- In a right-angled triangle, the square on the hypotenuse equals the sum of squares on the other two sides
- The hypotenuse is always the longest side in a right-angled triangle
- The hypotenuse is opposite to the right angle (90°)
Converse of Pythagoras Theorem
- If the square of the longest side equals sum of squares of other two sides, then the triangle is right-angled
- The right angle is opposite to the longest side
- This helps in verifying if a given triangle is right-angled
Triangle Classification Using Pythagoras Theorem
- Acute triangle: c² < a² + b² (where c is the longest side)
- Right triangle: c² = a² + b²
- Obtuse triangle: c² > a² + b²
Pythagorean Triplets
- Three positive integers a, b, c where a² + b² = c² are called Pythagorean triplets
- Common triplets: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
- Any multiple of a Pythagorean triplet is also a Pythagorean triplet
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