Similarity In Geometry

When there are two objects which have same shape, then the two objects are said to be geometrically similar and the Ratio of any two linear dimensions of one object is similar for any geometrically similar objects.
We can say the similar shape is just like congruent shapes in which they must be having same shape but it is not necessary that the size of the object is same, it may be different. Their Corresponding Angles are same and corresponding sides are in proportion. The similarity in Geometry shapes which are exactly same are congruent shapes Or we can say that two shapes are congruent when we can rotate, translate and reflect one of the shapes in such a way that it coincides exactly with the other shapes.
 

 
Hence, the shape when it may be reflected translated and rotated are congruent to its other part. These above two Triangles are congruent even though they are rotate in any direction. Similarity in Geometry shapes are identical in above case. The ratio of height to the hypotenuse of the triangle is same and all the dimensions of one triangle can be calculated by multiplying the dimensions of the other by a constant. It is a ratio that you get by dividing the corresponding side of one triangle by its other corresponding side in other similar triangle, it is known as similarity ratio. There are some rules for similarity in triangles.
Angle- angle similarity – if there are two triangles, if two angles of one triangle are congruent to the two angles of another triangle, then the triangles are similar.
Side-side-side similarity – there are two triangles, if all pairs of corresponding sides of two triangles are proportional, then the two triangles are similar.
In case of similar Polygon, in which all corresponding angles are congruent or same and all corresponding sides are proportional.