Triangles | Class 10 Mathematics Notes

Criteria for Similarity of Triangles

This section discusses the three main criteria used to establish the similarity of two triangles without having to measure all sides and angles. These criteria are essential tools in geometry for proving similarity efficiently. The three criteria are:

1. AAA (Angle-Angle-Angle) Criterion: If two triangles have their corresponding three angles equal, then the triangles are similar.

2. SAS (Side-Angle-Side) Criterion: If in two triangles, one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are in the same ratio, then the triangles are similar.

3. SSS (Side-Side-Side) Criterion: If the corresponding sides of two triangles are in the same ratio, then the triangles are similar.

These criteria help in establishing similarity without measuring all sides or angles. The section provides proofs and examples for each criterion, showing how to apply them in different problems. Understanding these criteria is crucial for solving many geometric problems involving triangles.

📊 Diagram: Fig. 6.3; Fig. 6.4; Fig. 6.5

🧪 Activity: Exercises involving proving similarity of triangles using AAA, SAS, and SSS criteria.

🔗 Connection: Leads to the section on applications of similarity of triangles in real-life problems.