Chapter 6 — Triangles

NCERT Class 10 Maths Chapter 6 covers similarity of triangles, including the Basic Proportionality Theorem (Thales Theorem) and three criteria for similarity — AAA, SSS, and SAS — with an application to proving the Pythagoras Theorem.

Chapter 6 of NCERT Class 10 Mathematics introduces similar figures — shapes that have the same form but not necessarily the same size. It establishes that two polygons are similar when their corresponding angles are equal and their corresponding sides are in the same ratio (scale factor). The chapter proves the Basic Proportionality Theorem (Thales Theorem): a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. It then develops three criteria for triangle similarity — AAA (Angle-Angle-Angle), SSS (Side-Side-Side), and SAS (Side-Angle-Side) — and applies them to real-world problems such as calculating shadow lengths and heights of distant objects.

1. 01Two figures are similar if they have the same shape but not necessarily the same size; all congruent figures are similar but not vice versa.
2. 02Two polygons are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (scale factor).
3. 03Basic Proportionality Theorem (Thales Theorem): a line parallel to one side of a triangle divides the other two sides in the same ratio; the converse is also true.
4. 04AAA Similarity Criterion: if corresponding angles of two triangles are equal, their corresponding sides are proportional and the triangles are similar.
5. 05SSS Similarity Criterion: if sides of one triangle are proportional to sides of another, their corresponding angles are equal and the triangles are similar.
6. 06SAS Similarity Criterion: if one angle of a triangle equals one angle of another and the sides including those angles are proportional, the triangles are similar.