a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
Question
A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
Solution
Understanding the Problem
We are looking for a quadrilateral that has rotational symmetry of order greater than 1, meaning it can be rotated by a certain angle and still appear unchanged, but does not exhibit line symmetry, meaning there are no lines of reflection that divide it into two identical halves.
Identifying Suitable Quadrilaterals
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Rotational Symmetry of Order Greater Than 1:
- A shape has rotational symmetry of order 2 if it can be rotated 180 degrees and looks the same. For order greater than 2, it must also appear identical at other angles (like 120 degrees for order 3).
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Line Symmetry:
- A shape has line symmetry if it can be divided into two identical parts by a line. We need to avoid this characteristic in our quadrilateral.
Example of a Suitable Quadrilateral
A kite without being a rhombus serves as a good example of a quadrilateral meeting these criteria. A kite has:
- Rotational Symmetry of Order 2: It looks the same when rotated by 180 degrees.
- Lacks Line Symmetry: In general, a kite does not have a line of symmetry unless special cases are considered (like a rhombus, which does not suit our needs).
Summary
A kite fulfills the criteria of having rotational symmetry (specifically of order 2) while not possessing line symmetry when it is not a rhombus. Other non-standard shapes that may exhibit such properties could be crafted, but they may lack regularity. Thus, a kite stands as a classic example.
Similar Questions
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