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Revision Notes

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.

43 questions22 flashcards5 concepts

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A visual representation of the area-based proof of Pythagoras Theorem, showing squares constructed on each side of a right-angled triangle, and how their areas relate.
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Key Topics to Revise

1

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°)
2

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
3

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
4

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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Full Notes

Key Concepts

In a rightThe hypotenuse is the longest sideOne method of proving the theoremAn alternative proof uses similar trianglesIf in any triangle

Frequently Asked Questions

What are the important topics in Pythagoras Theorem for ICSE Class 9 Mathematics?
Pythagoras Theorem covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Pythagoras Theorem — ICSE Class 9 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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