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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.

30 questions25 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

Core theorem and converse

  • In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
  • If BC^2 = AB^2 + AC^2 and BC is the largest side, then angle A = 90 degrees.
  • The converse is a right-angle test: if the square on the largest side equals the sum of the squares of the other two sides, the triangle is right-angled.
2

Proof ideas and key area facts

  • Theorem 9 gives an area based proof of Pythagoras Theorem.
  • In Triangle ABC with angle ABC = 90 degrees, squares are drawn on AC, AB, and BC.
  • Area of square ABFG equals area of rectangle AMNE.
3

Triangle type test and Pythagorean triplets

  • If AB is the largest side of triangle ABC, then AB^2 = AC^2 + BC^2 means the triangle is right-angled.
  • If AB^2 > AC^2 + BC^2, then the triangle is obtuse-angled.
  • If AB^2 < AC^2 + BC^2, then the triangle is acute-angled.
4

Solved application patterns

  • A ladder problem uses Pythagoras Theorem twice, once for each position of the ladder.
  • In the ladder problem, the ladder length is 17 m in both positions.
  • PA equals 8 m because 17^2 - 15^2 = 64.

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Full Notes

Key Concepts

In a rightIf in any triangleFor a rightDrawing a perpendicular from the rightIf a^2 + b^2 = c^2

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?
Understand the core concepts first, then work through the 30 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall 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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