 Welcome to the session. In this session we shall discuss about the similar figures. Two figures having the same shape but not necessarily the same size are called similar figures. Consider these two circles. These two figures have same shape but they don't have same size so they are the similar figures. Next we have two polygons of same number of sides are similar if falling two conditions are satisfied. The first one is their corresponding angles are equal. The second condition is their corresponding sides are in the same ratio. We know that a triangle is a polygon so we can also say that two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Consider these two triangles ABC and PQR. As you can see their corresponding angles are equal and their corresponding sides are in the same ratio so we say triangle ABC is similar to triangle PQR. Now let's discuss very important theorem which is basic proportionality theorem. According to this theorem we have that if a line is drawn parallel to one side of a triangle the other two sides in distinct points then the other two sides are divided in the same ratio. Given this triangle ABC if we draw a line parallel to the side BC of this triangle this is the line L we have drawn L parallel to the side BC of the triangle. This line intersects the other two sides at the points D and E. According to basic proportionality theorem we get that AD upon DB is equal to AE upon EC. That is the line L divides the two sides that is AB and AC of the triangle in the same ratio. Next we have converts of basic proportionality theorem. According to this we have if a line divides sides of a triangle in the same ratio then the line is parallel to the third side. Consider this triangle ABC this line L divides the two sides AB and AC of the triangle in the same ratio that is we have AD upon DB is equal to AE upon EC. Then according to the converts of basic proportionality theorem we get that the line L is parallel to the third side that is BC. This completes the session. Hope you have understood the concept of similar triangles, basic proportionality theorem and the converts of basic proportionality theorem.