(i). All circles are _________ (congruent, similar).

Solution:-

Both circles have the same shape but not the same size because all the circles have the same shape but the same size is not necessary. Hence all circles are similar, not congruent.

(ii). All squares are __________ (congruent, similar).

Solution:-

Both squares have the same shape but not the same size because all the squares have the same shape but the same size is not necessary. Hence all squares are similar, not congruent.

(iii). All __________ triangles are similar. (isosceles, equilateral).

Solution:-

Equilateral triangle – An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Triangle have 3 sides and 3 angles and in equilateral all sides and angles are equal so for making similar triangles same sides of a triangles must be equal. Hence all equilateral triangles are similar.

Isosceles triangle – An isosceles triangle is a triangle that has two sides of equal length. Triangle have 3 sides and in isosceles any two sides are equal but for making similar triangles same sides of a triangles must be equal.

(iv). Two polygons of the same number of sides are similar, if

1. Their corresponding angles are ________. (equal, proportional)
2. Their corresponding sides are _________.(equal, proportional)

Solution:-

A polygons are similar only if the corresponding angles are equal and the ratio of their corresponding sides are same.

1. Their corresponding angles are equal.
2. Their corresponding sides are proportional.