Congruence of plane figures.

Suppose, you are standing in front of a mirror.

The image formed in the mirror is always upright and is of the same shape and size as you.

You may prove it through superposition.

Which means, if you place yourself over the image, you and your image cover each other completely.

In mathematical terms, superposition is known as congruence.

Let’s learn more about this.

Let’s assume, we have two different shapes as shown above.

If we try to place one shape over the other, the shapes will never cover each other completely.

Now, let us take 2 triangles which are free to rotate on a plane.

If we rotate and try to overlap them, we can see that both of them will cover each other.

In this way, we can say that both are congruent to each other.

This phenomenon is called congruence.

Each geometrical figure has its own congruent shape.

For example, a square will have another square as its congruent shape.

Hence, we can conclude that two plane figures are congruent, if, each when superimposed on the other, covers it completely.

Revision

If two geometrical figures have the same shape and same size, then they are congruent to each other.

If we rotate and try to overlap them, we can see that both will cover each other completely.

In this way, we say that both are congruent to each other.

Each geometrical figure has its own unique congruent shape.

The End