Similarity
ICSE · Class 10 · Mathematics
Quick revision notes for Similarity — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Introduction to Similarity
- Similar figures have the same shape but may have different sizes
- All congruent figures are similar, but all similar figures are not necessarily congruent
- Similarity involves proportionality of corresponding parts
Criteria for Similarity of Triangles
- Three main criteria: AA (Angle-Angle), SAS (Side-Angle-Side), SSS (Side-Side-Side)
- AA Similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar
- SAS Similarity: If one angle and the two sides including it are proportional to the corresponding angle and sides of another triangle
Basic Proportionality Theorem (Thales' Theorem)
- If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally
- Converse: If a line divides two sides of a triangle proportionally, then it is parallel to the third side
- This theorem is fundamental for proving many similarity relationships
Angle Bisector Theorem
- The internal bisector of an angle in a triangle divides the opposite side in the ratio of the other two sides
- If AD is the angle bisector of ∠A in triangle ABC, then BD/DC = AB/AC
- Converse: If a line divides the opposite side in the ratio of the other two sides, then it bisects the angle
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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.
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