Congruence And Similarity

Robert finds two marbles that look exactly the same.
John has got a new baby. People visited him to congratulate John and say that the baby looks like him.
Note the two words exactly  and  looks like.
In mathematics these two words are defined as congruence and similarity.
Definition on Congruence and Similarity
Between congruence and similarity, let us see what is meant by similarity.
Two shapes are said to be similar if the shapes are same. The sizes may be different. The following is the example.

In the above diagram you find the two triangles look alike but the sizes are different. If the difference in size  is in a right proportion then the triangles are said to be similar.
That is, for the above triangles  to be similar, the ratio of the corresponding sides of the triangles must be same. Besides the measures of the angles must be equal.
Thus, the complete definition of similarity of two figures is both the figures must be of the same shape and the corresponding sides must be in the same ratio. Also the corresponding angles must be congruent.
The concept of similarity has many practical applications. You see a building. It is impossible to show the building to the same size on a drawing. What is normally done is to draw a smaller but the same shape of the building to a certain ratio. This ratio is called as the scale factor.
Definition on Congruence and Similarity
in congruence and similarity, we have seen what is meant by similarity of two figures.
If two figures are to be congruent, they must be of same shape and also of be same size.

In the above diagram you find the two triangles are of same shape and he measures of the corresponding sides and the measures of the corresponding angles are equal. Hence the two triangles can be said as congruent.
Thus, the complete definition of congrency of two figures is both the figures must be of the same shape and of the same size. Also the corresponding angles must be congruent.
Please note that the transformation of figures does not affect congruency.
The congruency of two shapes can be established if they fulfill certain geometric conditions. The concept of congruency helps in many geometric solutions.