Let us understand the concept of similar shapes using the below activity.
Take a cardboard and cut it into a triangular shape. Place the cardboard under the torchlight about \(1 \ m\) above the ground. We can see that the triangular cardboard forms a triangular image on the ground.
If we move the cardboard close to the ground, the image becomes smaller and smaller. If we move the cardboard away from the ground, the image becomes larger and larger.
We can see that the size of the angles forming the three vertices of the triangle would always be the same, even though their sizes are different.
This proves that two polygons of the same number of sides are similar, if
(i) all the corresponding angles are equal, and
(ii) all the corresponding sides are in the same ratio (or proportion).