Step 1: Verify the Congruent principle.

           NOTE: Two circles are congruent if they have the same size and shape.

          The size can be measured as the radius, diameter or circumference.

          They can overlap.

          Two circles are congruent if they have the same diameter

          So, All circle are not congruent.

Step 2: Check the similarity principle

          DEFINITION:  Two figures are similar means that they share a common shape. They can be different sizes, but they must have the same shape. For example, observe this image of the butterflies:

Similar Figures 1e

Step 3:  Prove that the all the squares are similar

            EXPLANATION:  Similar polygons have the same shape, but can be different sizes. Specifically, two polygons are similar if two things are true:

  1. The corresponding sides of each are in the same proportion
  2. The corresponding interior angles are the same (congruent).

So when you take a square and compare it with another square, all sides of 1st one are proportional to another. And all angles are of course 90 degrees.

So, Any two squares are similar because they have the common shape but they are in different sizes.