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Syllabus

Similarity — Syllabus

ICSE · Class 10 · Mathematics

What Similarity covers in ICSE Class 10 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 10 Mathematics syllabus.

40 questions24 flashcards5 formulas & key relations5 concepts

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A comparison illustrating the difference between congruent figures (same shape and size) and similar figures (same shape, different size), using examples of triangles and other polygons.
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4 Topics · ICSE Class 10 Mathematics · 2026-27

Topics in Similarity

1

1. Similar Figures and Similar Triangles

  • Figures that have the same shape but different size are called similar figures.
  • Same shape does not mean equal size.
  • Two triangles are similar if their corresponding sides are proportional and their corresponding angles are equal.
2

2. Conditions for Similarity of Triangles

  • There are three main similarity conditions: SSS, AAA, and SAS.
  • SSS similarity: three corresponding sides are proportional.
  • AAA similarity: corresponding angles are equal.
3

3. Basic Proportionality Theorem and Its Converse

  • Theorem 1: If a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides the other two sides proportionally.
  • The converse says: if a straight line divides any two sides of a triangle proportionally, then the line is parallel to the third side.
  • In the converse proof, the line DE is first assumed not parallel to BC, and a parallel line DP is drawn through D.
4

4. Internal Angle Bisector Theorem and Its Converse

  • The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
  • If AD is the internal bisector of ∠A in △ABC, then BD/DC = AB/AC.
  • In Theorem 3, CE is drawn parallel to DA meeting BA produced at E.

Key Concepts

Central concept: Similarity of triangles and similar figures

Similar figuresSimilarity of trianglesDifference between proportional and equalSimilarity conditionsCongruency and similarityBasic Proportionality TheoremConverse of Basic Proportionality TheoremInternal angle bisector theorem

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Frequently Asked Questions

What are the important topics in Similarity for ICSE Class 10 Mathematics?
Key topics in Similarity include Similar Figures and Similar Triangles, Conditions for Similarity of Triangles, Basic Proportionality Theorem and Its Converse, Internal Angle Bisector Theorem and Its Converse. Study these first, then practise questions on each for the ICSE Class 10 board exam.
How should I revise Similarity for the ICSE Class 10 board exam?
Learn the core ideas first, then work through the 40 practice questions on Similarity. 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 10 Mathematics Syllabus

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