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Chapter Summary

Inequalities — Chapter Summary

ICSE · Class 9 · Mathematics

Summary of Inequalities for ICSE Class 9 Mathematics. Part of the ICSE Class 9 Mathematics syllabus. Inequalities compare quantities that are not equal.

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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Overview

Inequalities compare quantities that are not equal. The signs greater than and less than are used to show the relation between numbers or lengths. In geometry, inequalities are especially important for triangles, where side lengths and angle sizes are closely linked. The chapter develops the idea th

Key Concepts

The sign > means is greater

The sign > means is greater than, and the sign < means is less than. These signs are used to compare numbers, lengths, and other quantities.

If two sides of a triangle

If two sides of a triangle are unequal, the greater side has the greater angle opposite to it. For triangle ABC, if AB>AC, then angle ACB is greater t

If two angles of a triangle

If two angles of a triangle are unequal, the greater angle has the greater side opposite to it. For triangle ABC, if angle CAB is greater than angle B

Of all the lines drawn from

Of all the lines drawn from a point outside a line to that line, the perpendicular is the shortest. If OP is perpendicular to AB and Q is any other po

The sum of the lengths

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

Learning Objectives

  • Understand the meaning of greater than and less than signs.
  • Use the relation between unequal sides and unequal angles in a triangle.
  • Apply the converse result: larger angles lie opposite larger sides.
  • Use the shortest-distance property of the perpendicular from a point to a line.
  • Apply triangle inequality results for sums and differences of sides.

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.

More resources for Inequalities

All ICSE Class 9 Mathematics Chapter Summary

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