Students are asked to establish a relation between vertically opposite angles. They draw various figures, measure the angles and observe that vertically opposite angles are equal.
In this case, students according to Van Hiele thought are at

Options

A. visualisation level
B. analytic level
C. informal deduction level
D. deduction level

Answer

To solve the question regarding the level of geometric thinking according to Van Hiele that students are demonstrating when they establish a relationship between vertically opposite angles, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vertically Opposite Angles**:
- Vertically opposite angles are formed when two lines intersect. The angles that are opposite each other at the intersection are called vertically opposite angles.

2. **Observation and Measurement**:
- Students draw various figures and measure the angles formed by intersecting lines. They observe that the angles opposite each other are equal.

3. **Identifying the Level of Geometric Thinking**:
- According to Van Hiele's levels of geometric understanding, we need to identify which level corresponds to the students' ability to recognize that vertically opposite angles are equal.

4. **Reviewing Van Hiele's Levels**:
- **Level 0 (Recognition)**: This level involves recognizing shapes and figures but does not involve understanding properties or relationships.
- **Level 1 (Analysis)**: At this level, students can analyze shapes and distinguish between different properties.
- **Level 2 (Informal Deduction)**: This level involves understanding relationships between properties, such as recognizing that a square is a type of rectangle.
- **Level 3 (Deduction)**: This level involves formal proofs and logical reasoning, which is more advanced.

5. **Determining the Correct Level**:
- Since the students are not just recognizing shapes but are also establishing a relationship (that vertically opposite angles are equal), they are operating at **Level 2 (Informal Deduction)**. This level allows them to understand and articulate the relationship between the angles.

6. **Conclusion**:
- Therefore, the answer to the question is that the students are at **Level 2 (Informal Deduction)** according to Van Hiele's levels of geometric thinking.