Based on the analysis of all eight shapes, I can now solve the problem. The task is to identify which of these figures have a point of symmetry.
A point of symmetry (or central symmetry) means that for every point on the figure, there is another point directly opposite it across the center, at the same distance. In other words, if you rotate the figure 180 degrees around this point, it will look exactly the same.
Let's evaluate each shape:
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(a): This is a broken line with triangles at the ends. It does not have a point of symmetry because rotating it 180 degrees would not map it onto itself.
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(b): Two intersecting lines. The intersection point is the center of symmetry. Rotating 180 degrees around this point maps the figure onto itself. So, it has a point of symmetry.
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(c): A triangle. A general triangle does not have a point of symmetry. Even an equilateral triangle only has rotational symmetry of 120 degrees, not 180 degrees. Therefore, it does not have a point of symmetry.
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(d): A pinwheel figure. Rotating it 180 degrees around the center maps it onto itself. So, it has a point of symmetry.
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(e): A cross shape. Rotating it 180 degrees around the center maps it onto itself. So, it has a point of symmetry.
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(f): A regular pentagon. A regular pentagon has rotational symmetry of 72 degrees, but not 180 degrees. Therefore, it does not have a point of symmetry.
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(g): A six-pointed star. Rotating it 180 degrees around the center maps it onto itself. So, it has a point of symmetry.
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(h): An abstract figure made of connected segments. It does not appear to have a point of symmetry; rotating it 180 degrees would not map it onto itself.
Therefore, the figures that have a point of symmetry are (b), (d), (e), and (g).
The solution to the problem is that shapes (b), (d), (e), and (g) have a point of symmetry.
Parent Tip: Review the logic above to help your child master the concept of rotational symmetry worksheet with answers.
