“Class 9 Mathematics Notes | Triangles – Congruency, Similarity & Pythagoras Theorem with Examples & Q&A”

Class 9 Mathematics Notes

Triangles: Congruency, Similarity & Pythagoras Theorem




1. Congruency of Triangles

👉 Two triangles are said to be congruent if all the
corresponding sides and angles are equal.

●​ Symbol: ≅​


Conditions for Congruency (Rules)

1.​ SSS (Side-Side-Side): If three sides of one triangle
are equal to three sides of another, then the triangles
are congruent.​

2.​SAS (Side-Angle-Side): If two sides and the included
angle are equal, then triangles are congruent.​

3.​ASA (Angle-Side-Angle): If two angles and the
included side are equal, then triangles are congruent.​

4.​AAS (Angle-Angle-Side): If two angles and a
non-included side are equal, then triangles are
congruent.​

5.​RHS (Right angle-Hypotenuse-Side): In
right-angled triangles, if hypotenuse and one side

, are equal, then triangles are congruent.​


✅ Example:​
In ΔABC and ΔDEF, if AB = DE, AC = DF, and ∠A = ∠D →
By SAS rule, ΔABC ≅ ΔDEF.



2. Similarity of Triangles

👉 Two triangles are said to be similar if:
1.​ Their corresponding angles are equal.​

2.​Their corresponding sides are in the same ratio.​

●​ Symbol: ~​


Conditions for Similarity

1.​ AAA (Angle-Angle-Angle): If two triangles have
equal corresponding angles, they are similar.​

2.​SSS (Side-Side-Side): If the sides of two triangles
are proportional, they are similar.​

3.​SAS (Side-Angle-Side): If one angle is equal and the
sides including these angles are proportional, the
triangles are similar.​