### Theory:

In the previous grade, we have learnt about congruent. Let us recall them.

 Two rectangles have the same side length; then, they are congruent. Two equilateral triangles have the same side lengths; then, they are congruent. Two cubes have the same side lengths; then, they are congruent.

Now, let us learn the concept of similar figures.

 Consider $$2$$ or more circles. From the figure, it is obvious that the radii are not the same, and are not congruent. But they are of the same shape.Hence, they are called similar shapes. Consider $$2$$ or more triangles. Here, the lengths of triangles are not the same, but they are of the same shape. Hence, they are called similar shapes. Consider $$2$$ or more rectangles. Here, the length and breadth of the rectangle are not the same, but they are of the same shape. Hence, they are called similar shapes.

From the above two tables, we can conclude that all congruent figures are similar, but the similar figures need not be congruent.

Now, can you say that a rectangle and a circle are similar shapes?

From the figures, we can say that they are not similar shapes.

There are certain definition of similarity of shapes. Based on this, we can decide whether the given figures are similar or not.
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.
Scale factor
A scale of an image of an object is the same shape of the object but in different size.

The scale of an image of an object is written in ratio which is a comparison of the length of the image to the length of the object.

In other words, a scale factor is defined as the ratio of the corresponding sides of similar figures.