(i) All circles are similar. (congruent, similar)
Reason: All circles have the same shape, regardless of their size (radius). Congruent circles must also have the same size.

(ii) All squares are similar. (similar, congruent)
Reason: All squares have the same shape (four equal sides and four right angles). They are only congruent if their side lengths are equal.

(iii) All equilateral triangles are similar. (isosceles, equilateral)
Reason: All equilateral triangles have all angles equal to 60°, so their corresponding angles are always equal, making them similar.

(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional. (equal, proportional)
Reason: This is the definition of similarity for polygons. Both conditions must be met.

(i) similar figures.
1. A pair of equilateral triangles, one with side 2 cm and another with side 4 cm.
2. A pair of squares, one with side 3 cm and another with side 5 cm.

(ii) non-similar figures.
1. A square and a rectangle. (Their corresponding angles are equal, but their corresponding sides are not proportional).
2. A triangle and a quadrilateral. (They do not have the same number of sides).

Step 1: Check if corresponding sides are proportional.
For quadrilateral PQRS and ABCD:
Ratio of sides = PQ/AB = QR/BC = RS/CD = SP/DA = 1.5/3 = 1/2.
The corresponding sides are in proportion.

Step 2: Check if corresponding angles are equal.
The angles of quadrilateral ABCD are all 90° (it’s a square).
The angles of quadrilateral PQRS are not 90° (it’s a rhombus, not a square). For example, ∠P is obtuse and ∠Q is acute.

Conclusion:
Since the corresponding angles are not equal, the two conditions for similarity are not met.

Answer: The quadrilaterals are not similar.