Question 8

Explanation

Let's analyze each plane figure based on the number of its reflectional and rotational symmetries.

The required conditions are:

1. Rotational symmetry $\ge 2$
2. Reflectional symmetry $\ge 3$

Scalene Triangle

• Reflectional symmetry: 0 (has no axis of symmetry).
• Rotational symmetry: 1 (only returns to original position after 360-degree rotation).

Conclusion: Does not satisfy both conditions.

Parallelogram Not a Rhombus

• Reflectional symmetry: 0 (has no axis of symmetry).
• Rotational symmetry: 2 (rotational symmetry of order 2).

Conclusion: Satisfies the rotational symmetry condition, but does not satisfy the reflectional symmetry condition.

Ellipse

• Reflectional symmetry: 2 (major and minor axes).
• Rotational symmetry: 2 (rotational symmetry of order 2).

Conclusion: Satisfies the rotational symmetry condition, but does not satisfy the reflectional symmetry condition (only has 2, requires at least 3).

Regular Hexagon

• Reflectional symmetry: 6 (has 6 axes of symmetry).
• Rotational symmetry: 6 (rotational symmetry of order 6).

Conclusion: Satisfies both conditions (rotational symmetry $6 \ge 2$ and reflectional symmetry $6 \ge 3$).

Final Conclusion

Of the four plane figures, only 1 plane figure satisfies the criteria, which is the Regular Hexagon.