After the completion of topic "Parallelograms" in a mathematics class, a student says. "A square is also a rectangle and that a rectangle is also a special type of parallelogram". The student is at which level of geometric reasoning according to Van Hieles theory of geometrical development?

Option 3 : Level 2 (Relationships)

The Van hiele theory explains how children learn geometry. It proposes 5 different levels of geometric thinking. Each level has its symbols and language. the levels are progressed "step by step" by the students. This hierarchical structure helps them in gaining better knowledge and achieving greater results in mathematics.

5 levels of understanding geometry:

• Visualization level- Students at this level identify and compare shapes based on their appearance as a whole.
• Analysis level- Children at this level recognize figures by their properties or components. For example, students will refer to figures as squares, since they both have 4 sides, 4 right angles, and equal and opposite sides among other qualities.
• Abstract or relationship level- At this level, students can define a figure using a minimum set of properties, make formal arguments (about different shapes), and deduce new properties.
• Formal deduction level- Students establish theorem within an axiomatic system. They can distinguish between undefined concepts, definitions, axioms, and theorems. They can create original proofs.
• Mathematical rigor level- Students are aware of the connections between diverse symmetrical systems. They can explain how adding or removing an axiom affects the geometric system and they are capable of comparing, analyzing, and creating proofs in a variety of geometric systems.

Hence, we conclude that according to Van hiele's theory of geometrical understanding the child is at the relationship level.