Take into account that only reflection over lines which cross the center of the polygon and the midpoints of opposite sides, will map the polygon onto itself (the same for lines which cross opposite vertex of the figure).
Then, from the given answer choices, the following ones are true:
- A reflecion across line b, trough one vertex, the center d.
- A reflection across line c, trough the midpoints of opposite sides.
Now, related to the rotation, if θ (the angle of rotation) is such an angle that 360/θ is an integer, and the number of sides of the figure is multiple of the integer, then, the polygon will map onto itself after the transformation.
For θ = 60 degrees, 360/60 = 6
For θ = 120 degress, 360/120 = 3
Then, the following is true:
- A rotation of 60 degrees around the center point d.
- A rotation of 120 degrees around the center point d.