Question 9

Explanation

Let's analyze the number of lines of symmetry (folding symmetry) and rotational symmetries for each given plane figure:

1. Isosceles right triangle

   • Lines of symmetry: $1$ (altitude from the right angle to the hypotenuse).
   • Rotational symmetries: $1$ (rotation of $360^\circ$).
   • Conclusion: The numbers are equal.

2. Right trapezoid

   • Lines of symmetry: $0$.
   • Rotational symmetries: $1$ (rotation of $360^\circ$).
   • Conclusion: The numbers are not equal.

3. Rectangle (not a square)

   • Lines of symmetry: $2$ (vertical and horizontal axes).
   • Rotational symmetries: $2$ (rotation of $180^\circ$ and $360^\circ$).
   • Conclusion: The numbers are equal.

4. Rhombus (not a square)

   • Lines of symmetry: $2$ (both diagonals).
   • Rotational symmetries: $2$ (rotation of $180^\circ$ and $360^\circ$).
   • Conclusion: The numbers are equal.

The figures that have the same number of rotational symmetries and lines of symmetry are:

1. Isosceles right triangle.
2. Rectangle.
3. Rhombus.

So, there are $3$ figures that satisfy the condition.