In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling, possibly with additional translation, rotation and reflection. In day-to-day life, we come across several objects which have something in common. Observing them closely, we can see that some of them have the same shape but may have the different or same size; such figures are called similar figures. Two triangles are said to be similar if their corresponding angles are equal and corresponding sides are proportional.
By using AAA similarity theorem, SSS similarity theorem and SAS similarity theorem, we can prove two triangles are similar. We now know that two triangles are similar if their corresponding angles are equal, and the corresponding sides are proportional. If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides. We shall learn more about theorems related to similar triangles in this topic. This chapter deals with the similarity of triangles. Basics of understanding corresponding sides and corresponding angles of similar triangles, various conditions for the similarity of two triangles, Basic Proportionality theorem, the relation between the areas of two triangles, similarity as a size transformation and finally the applications to maps and models are the key concepts covered under this chapter.