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Revision Notes

Similarity

ICSE · Class 10 · Mathematics

Quick revision notes for Similarity — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

40 questions24 flashcards5 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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Key Topics to Revise

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.

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Full Notes

Key Concepts

Figures that have the same shapeTwo triangles are similar if theirCorresponding sides can be proportional withoutCongruent figures have the same shapeIf three sides of one triangle

Frequently Asked Questions

What are the important topics in Similarity for ICSE Class 10 Mathematics?
Similarity covers several key topics that are frequently asked in ICSE Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Similarity — ICSE Class 10 Mathematics?
Understand the core concepts first, then work through the 40 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.

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