180°
A rotation of 360 degrees will map a parallelogram back onto itself.
Itself
Rotation
Ft
Linear transformation is a function between vector spaces that will always map a parallelogram onto itself. Some examples are rectangles and regular polygons.
A trapezoid
Yes
An isosceles trapezium (or isosceles trapezoid) has an order of rotational symmetry of 1. This means it can only be rotated 360 degrees to look the same at one position, as it does not map onto itself at any other angle of rotation. In contrast, shapes with higher rotational symmetry can appear the same at multiple angles.
A square.
A rotation of 360 degrees will map a parallelogram back onto itself.
Itself
Rotation
Ft
Linear transformation is a function between vector spaces that will always map a parallelogram onto itself. Some examples are rectangles and regular polygons.
A common transformation that will map any parallelogram onto itself is a rotation by 180 degrees about its center. This rotation preserves the shape and size of the parallelogram while repositioning it in such a way that every vertex moves to the location of the opposite vertex. Additionally, reflections across the diagonals or the midpoints of opposite sides also map the parallelogram onto itself.
For translation, the only transformation (not transfermation), is the null translation (0,0).
A transformation that will always map a parallelogram onto itself is a rotation by multiples of 180 degrees around its center. This rotation preserves the lengths of the sides and the angles, maintaining the shape and position of the parallelogram. Additionally, reflections across the lines of symmetry or the diagonals will also map a parallelogram onto itself.