Class 9 · Chapter 7

Triangles

Congruence of triangles; SSS, SAS, ASA, AAS, RHS; properties of isosceles triangles; triangle inequality.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

Two triangles are congruent if they have exactly the same shape and size — corresponding sides and angles are equal. Notation:

\triangle ABC \cong \triangle DEF

means

A\to D, B\to E, C\to F

with

AB=DE, BC=EF, CA=FD

and matching angles.

Key concepts & formulas

SSS, SAS, ASA, AAS, RHS are congruence criteria.

In an isosceles triangle, angles opposite equal sides are equal.

Sum of any two sides of a triangle

>

third side.

Larger side is opposite the larger angle.

In an equilateral triangle, all angles

= 60^\circ

Congruent triangles are also similar (with scale

1