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Parallelograms - including special cases.

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Which quadrilaterals always have both line symmetry and rotational symmetry?

The quadrilaterals that always have both line symmetry and rotational symmetry are squares and rectangles. Squares have four lines of symmetry and rotational symmetry of order 4, while rectangles have two lines of symmetry and rotational symmetry of order 2. Other quadrilaterals, like rhombuses and parallelograms, may have one type of symmetry but not both. Thus, squares and rectangles are the only quadrilaterals that consistently possess both symmetries.


What quadrilaterals have a rotational symmetry of order 4?

A quadrilateral with a rotational symmetry of order 4 is one that can be rotated 90 degrees, 180 degrees,270 degrees, and 360 degrees onto itself. The most common examples of such quadrilaterals are the square and the rhombus. In these shapes, each rotation results in the same appearance, demonstrating their high degree of symmetry.


What shapes have 1 order of rotational symmetry?

Nothing has 1 order of rotational symmetry because in rotational symmetry 1 is none.


Is triangle and square have line of symmetry and rotational line of symmetry?

Yes, both triangles and squares have lines of symmetry and rotational symmetry. An equilateral triangle has three lines of symmetry and a rotational symmetry of order 3, meaning it can be rotated by 120 degrees and still look the same. A square has four lines of symmetry and a rotational symmetry of order 4, allowing it to be rotated by 90 degrees and still appear unchanged. Other types of triangles and quadrilaterals may have different numbers of symmetries based on their specific shapes.


An equilateral triangle has reflectional symmetry but does not have rotational symmetry?

It does have rotational symmetry of order three.