Similar Polygons

In similar polygons, there are two aspects: ‘similarity’ and ‘polygon’. As we have already learned about polygons, here, let us understand what ‘similarity’ means.

What is Similarity in Polygons

In mathematics, a pair of polygons are said to be similar when their:

1. Corresponding angles are congruent
2. Corresponding sides are proportional

The symbol ∼ is commonly used to represent similarity.

Let’s take an example of two squares given below,

The four interior angles of one square are identical to the other. Also, their sides are found to be proportional. The smaller square could scale up to become the larger square. The two squares are thus similar.

E.g. 1. Prove whether the given pairs of rhombus are similar.

In rhombus ABCD,
∠ABC = ∠ADC… (1)
∠BAD = ∠BCD… (2) and,
AB = BC = CD = DA = 4 cm
In rhombus EFGH,
∠EFG = ∠EHG… (3)
∠FEH = ∠FGH… (4) and,
EF = FG = GH = HE = 2 cm

Taking together (1), (2), (3), (4), we can say that corresponding angles of rhombus ABCD and EFGH are congruent, and also the corresponding sides are proportional.
Hence, rhombus ABCD and EFGH are similar (Proved).

Scale Factor of Similar Polygons

In similar polygons, the scale factor is the ratio of one side of a polygon to the corresponding side of the other polygon.

How to Find the Scale Factor

When the corresponding sides of the polygons are similar, the number of times the smaller sides of one polygon becomes the larger sides of the other is their scale factor.