To determine if the figure described has the specified types of symmetry, let's consider each type one by one based on the characteristics of the star-like structure formed by the quadrilaterals.
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Reflectional symmetry with line h: If line h is the vertical axis that bisects the figure, you would need to check if one side of the figure is a mirror image of the other when folded along this line. Given that the structure is symmetrically constructed, it is likely to have reflectional symmetry along line h.
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Reflectional symmetry with line g: If line g represents a different bisector (perhaps diagonal), you need to check whether the figure is symmetric about this line as well. If the quadrilaterals are symmetrically arranged around this diagonal, then yes, there would be reflectional symmetry.
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Reflectional symmetry with line m: Similar to line g, check if the star shape has mirrored halves about line m. If it does, then there is reflectional symmetry here as well.
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Reflectional symmetry with line n: Line n is the horizontal axis. For there to be reflectional symmetry along this line, the upper part of the figure should match the lower part exactly. If the structure is contoured symmetrically about the horizontal center, then reflectional symmetry will be present.
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90˚ rotational symmetry: A figure has 90˚ rotational symmetry if it looks the same after being rotated 90 degrees around a center point. If the quadrilaterals are arranged to face in four different directions symmetrically, then the figure likely has this symmetry.
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120˚ rotational symmetry: 120˚ rotational symmetry implies that the figure maintains its appearance after being rotated by 120 degrees. Given that there are three quadrilaterals forming a star shape, this symmetry is likely present since rotating by 120 degrees would align the quadrilaterals back into their original position.
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180˚ rotational symmetry: The figure has 180˚ rotational symmetry if it looks the same after a half-turn around a central point. If the quadrilaterals pair up across the center of the figure, this symmetry usually exists in such designs.
In summary, the type of symmetry present in the described star-like structure would need to be checked against these criteria based on the actual layout of the quadrilaterals. Most likely, it will exhibit reflectional symmetry along the specified lines (if appropriately mirrored), and it likely possesses both 120° and 180° rotational symmetry due to the three-fold symmetry in arrangement.