Problem:
The task is to determine the
order of rotational symmetry for each of the given shapes. The order of rotational symmetry is defined as the number of times a shape looks exactly the same during a full rotation (360°).
Steps to Solve:
####
Shape 1:
- The first shape is a circle with four overlapping arcs.
- A circle has infinite rotational symmetry because it looks the same at any angle of rotation.
- However, in this specific case, the overlapping arcs create a pattern that repeats every 90°.
- To find the order of rotational symmetry:
- Rotate the shape by 90°: It looks the same.
- Rotate by another 90° (total 180°): It looks the same.
- Rotate by another 90° (total 270°): It looks the same.
- Rotate by another 90° (total 360°): It returns to its original position.
- The pattern repeats 4 times in a full rotation.
-
Order of rotational symmetry = 4
####
Shape 2:
- The second shape is a star-like figure composed of triangles.
- To determine the order of rotational symmetry:
- Observe the structure: The shape has 6 triangular points radiating outward.
- Rotate the shape by 60°: It looks the same.
- Rotate by another 60° (total 120°): It looks the same.
- Rotate by another 60° (total 180°): It looks the same.
- Rotate by another 60° (total 240°): It looks the same.
- Rotate by another 60° (total 300°): It looks the same.
- Rotate by another 60° (total 360°): It returns to its original position.
- The pattern repeats 6 times in a full rotation.
-
Order of rotational symmetry = 6
####
Shape 3:
- The third shape is a cross-like figure with four identical arms.
- To determine the order of rotational symmetry:
- Observe the structure: The shape has four symmetrical arms.
- Rotate the shape by 90°: It looks the same.
- Rotate by another 90° (total 180°): It looks the same.
- Rotate by another 90° (total 270°): It looks the same.
- Rotate by another 90° (total 360°): It returns to its original position.
- The pattern repeats 4 times in a full rotation.
-
Order of rotational symmetry = 4
Final Answer:
\[
\boxed{4, 6, 4}
\]
Parent Tip: Review the logic above to help your child master the concept of line and rotational symmetry worksheet.
