Jasmine said, “A rectangle has two pairs of opposite sides parallel; a square also has two pairs of opposite sides parallel and so does a parallelogram. So, both rectangle and square are also parallelograms.”
Jasmine is at _________ stage of Van Hieles theory of geometric thinking.

The correct answer is Relationships.

Step-by-Step Explanation:

1. Understanding Van Hiele's Theory of Geometric Thinking:
Dutch educators Pierre van Hiele and Dina van Hiele-Geldof proposed a model describing how students learn geometry across five sequential levels (often numbered 0 to 4 or 1 to 5):

• Level 0 (Visualization / Recognition): Students recognize geometric shapes based on their overall visual appearance as a whole (e.g., "It is a square because it looks like a box").
• Level 1 (Analysis): Students analyze shapes based on their properties and components (e.g., "A rectangle has 4 right angles and equal opposite sides"), but they treat shapes independently without recognizing class inclusions.
• Level 2 (Relationships / Informal Deduction / Abstraction): Students perceive relationships between properties and between different shapes. They understand class inclusions, such as recognizing that every square is a rectangle or that both rectangles and squares are special types of parallelograms because they share common properties.
• Level 3 (Formal Deduction): Students understand the role of axioms, theorems, definitions, and formal proofs.
• Level 4 (Rigor): Students can compare different axiomatic systems (non-Euclidean geometries) at an abstract level.

2. Analyzing Jasmine's Reasoning:
Jasmine observes:
- A rectangle has two pairs of opposite sides parallel.
- A square has two pairs of opposite sides parallel.
- A parallelogram has two pairs of opposite sides parallel.
From these properties, Jasmine connects the definitions and concludes: "So, both rectangle and square are also parallelograms."

3. Conclusion:
Because Jasmine is relating properties across different shapes to establish class inclusion (that squares and rectangles belong to the broader category of parallelograms), she is operating at the Relationships (Abstraction/Informal Deduction) stage of Van Hiele's theory.