CAT Similar Figures and Criteria for Similarity of Triangles - Practice Questions & MCQ

Similar Figures

Geometric figures which have the same shape but different sizes are known as similar fi gures. Two congruent figures are always similar but two similar figures need not be congruent.

For example: 

1. Any two line segments are similar.
2. Any two equivalent triangles are similar.
3. Any two squares are similar.

Two circles C1 and C2 are similar since their shapes are the same. 

C1 and C2 may have an equal area. 

While considering the circles C1 and C3 they may not be of equal area, but their shapes are the same.

C1 and C2 are of the same shape and of the same size.

C1 and C3 are of the same shape but of different sizes.

In both cases, they are of the same shape. Hence C1, C2, and C3 are similar circles.

Similar Polygone

Two polygons having the same number of sides are said to be similar, if

1. their corresponding angles are equal, and
2. the lengths of their corresponding sides are in the same ratio or proportional.

If two polygons ABCDE and PQRST are similar, we write, ABCDE ~ PQRST, where the symbol ‘~’ stands for ‘is similar to’

Similarity of Triangles

Two triangles are similar, if

1. their corresponding angles are equal and
2. their corresponding sides are in the same ratio (or proportion).

Note that if the corresponding angles of two triangles are equal, then they are known as equiangular triangles.

A famous Greek mathematician Thales gave an important truth relating to two equiangular triangles which is as follows:

The ratio of any two corresponding sides in two equiangular triangles is always the same.