To determine whether the star-like structure described in your image has the types of symmetry mentioned, we will analyze them one by one.
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Reflectional symmetry with line h: Yes, if line h is the vertical axis and each quadrilateral is arranged symmetrically about this line.
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Reflectional symmetry with line g: This depends on the orientation of line g. If it is a diagonal that divides the structure symmetrically, then yes; otherwise, no.
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Reflectional symmetry with line m: Similar to line g, if line m is a line of symmetry, then yes; otherwise, no.
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Reflectional symmetry with line n: If line n is the horizontal axis and the structure is symmetrical about this line, then yes.
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90˚ rotational symmetry: For the structure to have 90˚ rotational symmetry, it needs to look the same after a quarter turn. Given that it’s made of similar quadrilaterals, if they are arranged correctly, then yes.
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120˚ rotational symmetry: For the star-like structure to possess this, it must look the same when rotated by 120˚. If it is composed of 3 similar parts (as suggested by "three similar quadrilaterals"), then yes.
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180˚ rotational symmetry: If the structure can be rotated 180˚ and looks the same, then yes.
In summary, to completely confirm the symmetries, one would need to visualize the actual geometric shapes and orientations described, but generally speaking, based on the descriptions:
- Reflectional symmetry with line h: Yes
- Reflectional symmetry with line g: Depends on orientation (possible yes or no)
- Reflectional symmetry with line m: Depends on orientation (possible yes or no)
- Reflectional symmetry with line n: Yes (if symmetric about the horizontal)
- 90˚ rotational symmetry: Yes (if arranged appropriately)
- 120˚ rotational symmetry: Yes (if three identical parts)
- 180˚ rotational symmetry: Yes (if the structure facilitates it)
It seems that most symmetries could likely apply, but confirm visually based on the specific arrangement in the figure.