Triangles | Class 10 Mathematics Notes

Similarity of Triangles

Similarity of triangles is a fundamental concept in geometry where two triangles have the same shape but not necessarily the same size. This means their corresponding angles are equal, and the lengths of their corresponding sides are in the same ratio. Two triangles are said to be similar if their corresponding angles are equal and the ratios of the lengths of their corresponding sides are equal. This property is very useful because it allows us to compare triangles and solve problems involving indirect measurements. For example, if two triangles are similar, then the ratio of any two corresponding sides in one triangle is equal to the ratio of the corresponding sides in the other triangle. The concept of similarity extends beyond triangles to other polygons as well, but triangles are the simplest and most commonly studied case. The chapter explains this concept with examples and visual illustrations, such as photographs of the same monument in different sizes, demonstrating similarity in real life.

📊 Diagram: Fig. 6.1; Fig. 6.2; You will at once say that they are the photographs of the same monument (Taj Mahal) but are in different sizes. Would you say that the three photographs are similar? Yes, they are.

🧪 Activity: Observation of photographs of the Taj Mahal in different sizes to understand similarity.

🔗 Connection: Introduces the criteria for similarity of triangles, which are discussed in the next section.