Question 4

Explanation

We will analyze the number of lines of symmetry and rotational symmetries for each plane figure. The requirement is to have at most $2$ lines of symmetry and $2$ rotational symmetries.

Analyzing Right Trapezoid

A right trapezoid has no axis of symmetry and no rotational symmetry of higher order (only order $1$, which is the initial position).

• Lines of symmetry: $0$
• Rotational symmetry: $1$

This figure satisfies the condition (since $0 \le 2$ and $1 \le 2$).

Analyzing Regular Pentagon

A regular pentagon has $5$ equal sides.

• Lines of symmetry: $5$
• Rotational symmetry: $5$

This figure does not satisfy the condition.

Analyzing Equilateral Triangle

An equilateral triangle has $3$ equal sides.

• Lines of symmetry: $3$
• Rotational symmetry: $3$

This figure does not satisfy the condition.

Analyzing Kite (Not a Square)

A kite has one main axis of symmetry.

• Lines of symmetry: $1$
• Rotational symmetry: $1$

This figure satisfies the condition.

Conclusion

The plane figures that satisfy the condition are:

1. Right trapezoid.
2. Kite (not a square).

Thus, there are $2$ plane figures that satisfy the condition.