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Inequalities

ICSE · Class 9 · Mathematics

Complete topic list for Inequalities in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

28 questions25 flashcards5 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

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

Frequently Asked Questions

What are the important topics in Inequalities for ICSE Class 9 Mathematics?
Inequalities 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 Inequalities — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 28 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.

More resources for Inequalities

All 28 chapters — ICSE Class 9 Mathematics Syllabus

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