Revision Notes: Class 10 Maths Chapter 6 Triangles

A fast, one-glance recap of Class 10 Maths Chapter 6 (Triangles) — for the full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 6 notes are ideal for quick revision just before exams.

Last Updated: July 21, 2026

Why This Chapter Matters

Triangles is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

Revision Notes: Triangles

• Similar figures: same shape, not necessarily same size; congruent figures are always similar, but similar figures need not be congruent
• Similarity of polygons: corresponding angles equal and corresponding sides proportional — both conditions needed together
• Basic Proportionality Theorem (BPT / Thales’ Theorem): a line parallel to one side of a triangle divides the other two sides in the same ratio
• Converse of BPT: if a line divides two sides of a triangle in the same ratio, it is parallel to the third side
• Similarity criteria: AA (AAA), SSS, SAS
• Midpoint theorem (via BPT): a line through the midpoint of one side, parallel to another side, bisects the third side — and its converse
• Ratio of areas of similar triangles = square of the ratio of corresponding sides (beyond the current 3-exercise syllabus, but a key extension — see Extra Questions)
• Pythagoras theorem via similarity: the altitude to the hypotenuse of a right triangle creates two smaller triangles, each similar to the original and to each other
• Height-shadow / pole problems: use similar triangles formed by the sun’s rays at the same instant — ratio of height to shadow length is constant at a given time
• 2023 rationalisation removed old Exercises 6.4-6.6 (Areas of Similar Triangles, Pythagoras Theorem, Optional) — only 6.1, 6.2, 6.3 remain as numbered exercises now

See also: Extra Questions (HOTS) | Formulas Handbook

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Written by Satish

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