Check the relation `rho` for reflexive, symmetry and transitivity:
`alpha rho beta` iff `alpha` is perpendicular to `beta`, where `alpha` and `beta` are straight lines in a plane.

Explanation

To check the relation \( \rho \) for reflexivity, symmetry, and transitivity, we will analyze the definition of the relation: \( \alpha \rho \beta \) if and only if \( \alpha \) is perpendicular to \( \beta \), where \( \alpha \) and \( \beta \) are straight lines in a plane.

### Step 1: Check for Reflexivity
A relation is reflexive if every element is related to itself. In this case, we need to check if any line \( \alpha \) is perpendicular to itself.

- **Analysis**: A line cannot be perpendicular to itself because the angle between a line and itself is \( 0^\circ \) (not \( 90^\circ \)).
- **Conclusion**: Since no line \( \alpha \) is perpendicular to itself, the relation \( \rho \) is **not reflexive**.

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