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Syllabus

Inequalities — Syllabus

ICSE · Class 9 · Mathematics

What Inequalities covers in ICSE Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 9 Mathematics syllabus.

28 questions25 flashcards12 formulas & key relations5 concepts

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A diagram illustrating Theorem 3: If two sides of a triangle are unequal, the greater side has the greater angle opposite to it. Show triangle ABC with AB > AC, and highlight the angles opposite to th
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4 Topics · ICSE Class 9 Mathematics · 2026-27

Topics in Inequalities

1

1. Basic Symbols and Meaning

  • The sign > means is greater than.
  • The sign < means is less than.
  • These symbols are used to compare numbers, lengths, and angles.
2

2. Triangle Side-Angle Relationships

  • If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
  • If two angles of a triangle are unequal, the greater angle has the greater side opposite to it.
  • These two results are used again and again in proof-based questions.
3

3. Perpendicular from an Outside Point

  • Of all the lines drawn from a point outside a line to that line, the perpendicular is the shortest.
  • In right triangle OPQ, the right angle is the greatest angle.
  • A line drawn from the outside point O to the line AB is shortest when it is perpendicular to AB.
4

4. Triangle Inequality Results

  • The sum of the lengths of any two sides of a triangle is always greater than the third side.
  • The difference between the lengths of any two sides of a triangle is always less than the third side.
  • For triangle ABC, AB + AC > BC, AB + BC > AC, and BC + AC > AB.

Key Concepts

Central concept: Inequalities in triangles and their applications to sides, angles, medians, perpendicular distances, and interior points

Greater than and less than signsTheorem 3Theorem 4Theorem 5Corollary 1Corollary 2Angle bisector resultsMedian inequality

Work through every topic in Inequalities with notes and quizzes

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Frequently Asked Questions

What are the important topics in Inequalities for ICSE Class 9 Mathematics?
Key topics in Inequalities include Basic Symbols and Meaning, Triangle Side-Angle Relationships, Perpendicular from an Outside Point, Triangle Inequality Results. Study these first, then practise questions on each for Class 9 exams.
How should I revise Inequalities for Class 9 exams?
Learn the core ideas first, then work through the 28 practice questions on Inequalities. 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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All ICSE Class 9 Mathematics Syllabus

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