Question
45. Jasmine said, “A rectangle has two pairs of opposite sides parallel; a square also has two pairs of opposite sides parallel and similarly a parallelogram also has. Therefore both a rectangle and a square will be parallelograms.” Jasmine is at the level of geometric thinking of Van Hiele’s theory.
(1) Formal deduction
(2) Visualization
(3) Analysis
(4) Understanding of relations
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उत्तर : (4) Understanding of relations
कारण: Van Hiele levels of geometric thought are:
Level 0: Visualization: Recognizing shapes by their overall appearance, without focusing on their properties.
Level 1: Analysis: Identifying properties of shapes, but not understanding the relationships between them.
Level 2: Understanding of relations / Informal Deduction: Understanding relationships between properties of shapes and defining one type of shape from another (e.g., why rectangles and squares are parallelograms). Jasmine is doing exactly this – she is classifying rectangles and squares as parallelograms based on their properties.
Level 3: Formal deduction: Providing geometric proofs through formal deduction.
Level 4: Rigor: Understanding the relationships between different geometric systems.
Jasmine is using the properties of shapes (opposite sides being parallel) to understand their hierarchical relationships (rectangles and squares being parallelograms), which falls under Level 2 (Understanding of relations).
कारण: Van Hiele levels of geometric thought are:
Level 0: Visualization: Recognizing shapes by their overall appearance, without focusing on their properties.
Level 1: Analysis: Identifying properties of shapes, but not understanding the relationships between them.
Level 2: Understanding of relations / Informal Deduction: Understanding relationships between properties of shapes and defining one type of shape from another (e.g., why rectangles and squares are parallelograms). Jasmine is doing exactly this – she is classifying rectangles and squares as parallelograms based on their properties.
Level 3: Formal deduction: Providing geometric proofs through formal deduction.
Level 4: Rigor: Understanding the relationships between different geometric systems.
Jasmine is using the properties of shapes (opposite sides being parallel) to understand their hierarchical relationships (rectangles and squares being parallelograms), which falls under Level 2 (Understanding of relations).
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