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: October 24, 2026

Common Mistakes Students Make in Triangles

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

Similar triangles: same shape, corresponding angles equal and sides proportional.

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.

Frequently Asked Questions

What is the Basic Proportionality Theorem (Thales’ Theorem) used for?
It states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides, it divides those two sides in the same ratio — this single theorem and its converse are the basis for most similarity proofs in this chapter.

What is the difference between congruent and similar triangles?
Congruent triangles are identical in both shape AND size (all corresponding sides and angles are equal); similar triangles have the same shape but not necessarily the same size (corresponding angles are equal, and corresponding sides are in the same proportion).

What to Revise First (and Last) in This Chapter

Written by Satish

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