Successful people do what unsuccessful people are not willing to do. Don’t wish it were easier, wish you were better. – **Jim Rohn**

In this chapter you have studied the following points : **1.** Two figures having the same shape but not necessarily the same size are called similar figures.**2.** All the congruent figures are similar but the converse is not true. **3.** Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (i.e., proportion).**4.** If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.**5.** If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.**6.** If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion).**7.** If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion).

**8.** If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar (SSS similarity criterion).**9.** If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar (SAS similarity criterion).**10.** The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.**11.** If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other.**12.** In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem).**13.** If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.