Similar Polygons are Polygons which have the same size but may differ in size. We do use similar smaller figures to represent larger real life objects to solve problems related to it. A rectangular field is indicated by a small rectangle in your book to describe the problem. The actual field and the Book-figure are thus similar polygons. (The Book rectangle is nevertheless labeled with original dimensions). Proportions of corresponding sides are used to solve problems related to similar polygons.

Polygons with similar shape but may differ in size are called similar polygons.
Two Polygons with one to one correspondence between the vertices are similar if
  1. Each pair of corresponding angles are congruent.
  2. The measures of corresponding sides are proportional.

Similar Polygons Definitions

The symbol ∼ reads as 'similar to'. In the above diagram ABCD ∼ PQRS.
The order of vertices on either side of the similarity statement determines the corresponding vertices and hence the corresponding angles and sides. Using the definition of similarity for the above situation
∠A  ∠P,   ∠B  ∠Q,   ∠C  ∠R,   ∠D  ∠S.                    (Corresponding angles are congruent)

$\frac{AB}{PQ}$ = $\frac{BC}{QR}$ = $\frac{CD}{RS}$ = $\frac{DA}{SP}$         (Lengths of corresponding sides are proportional).

If each of the ratio given in the extended proportion above = k, then k is known as the scale factor of similarity or constant of proportionality.

The similar polygons may be repositioned by sliding, flipping or turning in order to identify the corresponding parts easily.