According to Van Hiele’s levels of development of geometrical thinking, which of the following represents level–2 (relationships)?

The correct option is: A child can informally deduce general properties of a given geometrical shape and is able to see the linkages among these properties.

To understand why this is the correct representation, let us look at the Van Hiele model of geometric thought. The model describes five levels of thinking through which students progress when learning geometry:

1. Level 0 (Visualization): Students recognize shapes as a whole based on their visual appearance rather than their properties. For example, a child identifies a square because it "looks like a box".
2. Level 1 (Analysis): Students begin to analyze the properties of shapes. They understand that a shape has specific components and attributes (e.g., a rectangle has four right angles and opposite equal sides). However, they cannot yet see the relationship between different shapes or their properties.
3. Level 2 (Relationships / Informal Deduction): Students can establish relationships between properties within a shape and among different shapes. They can make informal, logical arguments and deduce properties of shapes. For instance, they realize that because a square has all the properties of a rectangle, a square is also a rectangle. They understand the linkages and hierarchy among geometric properties.
4. Level 3 (Deduction): Students understand the significance of deduction, definitions, axioms, theorems, and proofs. They can construct formal proofs rather than just informal arguments.
5. Level 4 (Rigor): Students can work in different axiomatic systems and compare them. This is the most abstract level of geometric reasoning.

By comparing the levels, we find that the description of Level 2 (Relationships) corresponds directly to the ability of a child to informally deduce general properties of a geometrical shape and understand the linkages or connections among these properties.