Fill in the blanks:

(i) All circles are ……….

(ii) All squares are ………..

(iii) All ……… triangles are similar.

(iv) Two polygons with same number of sides are similar if

(a) …………………… (b)……………………

(i) All circles are similar.

Let there be two circles of radii r₁ and r₂.

Now, shifting the centre of smaller circle to the bigger circle.

If we slowly increase the radius of smaller circle, it will coincide with bigger circle when r₂ = r₁. Thus, the circles are similar.

(ii) All squares are similar.

Let there be two squares ABCD and EFGH. When the smaller square is kept at the centre of the square ABCD, then on increasing the side of EFGH both of them will coincide. Thus, they are similar.

Two polygons are similar if their corresponding are equal. The corresponding angles of the squares are 90°. Thus, they are similar.

(iii) All equiangular triangles are similar.

Two equiangular triangles have equal corresponding angles. Thus, they are similar by AA or AAA Similarity Rule.

(iv) Two polygons with same number of sides are similar if

(a) their all the corresponding angles are equal

(b) their corresponding sides are in the same ratio