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Syllabus

Pythagoras Theroem — Syllabus

ICSE · Class 7 · Mathematics

What Pythagoras Theroem covers in ICSE Class 7 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 7 Mathematics syllabus.

71 questions24 flashcards9 formulas & key relations5 concepts

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4 Topics · ICSE Class 7 Mathematics · 2026-27

Topics in Pythagoras Theroem

1

1. Hypotenuse and Basic Idea

  • In a right-angled triangle, the side opposite the angle of 90 degrees is called the hypotenuse.
  • The hypotenuse is always the largest side of the triangle.
  • In triangle ABC with angle ABC = 90 degrees, side AC is the hypotenuse.
2

2. Statement of Pythagoras Theorem

  • In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • This is the main rule used for finding unknown sides.
  • When the right angle is at A in triangle ABC, BC is the hypotenuse and BC^2 = AB^2 + AC^2.
3

3. Finding a Missing Side - Solved Examples

  • Example 2: In triangle XYZ right-angled at Z, XY = 15 cm and XZ = 9 cm, so YZ = 12 cm.
  • Example 3: In triangle PQR right-angled at R, PQ = 25 cm and QR = 20 cm, so PR = 15 cm.
  • When the hypotenuse is given, subtract the square of the known side from the square of the hypotenuse.
4

4. Testing Whether a Triangle is Right-Angled

  • A triangle with sides 20 cm, 9 cm and 12 cm is not right-angled.
  • The longest side is 20 cm.
  • Compare 20^2 with 9^2 + 12^2.

Key Concepts

Central concept: Pythagoras Theorem

HypotenuseRight-angled trianglePythagoras theoremConverse of Pythagoras theoremHistorical noteWorked examplesTriangle conditionsCommon mistakes

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Frequently Asked Questions

What are the important topics in Pythagoras Theroem for ICSE Class 7 Mathematics?
Key topics in Pythagoras Theroem include Hypotenuse and Basic Idea, Statement of Pythagoras Theorem, Finding a Missing Side - Solved Examples, Testing Whether a Triangle is Right-Angled. Study these first, then practise questions on each for Class 7 exams.
How should I revise Pythagoras Theroem for Class 7 exams?
Learn the core ideas first, then work through the 71 practice questions on Pythagoras Theroem. Revise 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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