A fast, one-glance recap of Class 10 Maths Chapter 6 (Triangles) — for the full worked explanations, see the Solutions.
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
