Problem 18

Explanation

We will determine the number of lines of symmetry and the order of rotational symmetry for each given plane figure.

Analysis of Isosceles Trapezoid

• Lines of Symmetry: Has $1$ line of symmetry (vertical line in the middle).
• Rotational Symmetry: Order $1$ (returns to original position only after $360^\circ$ rotation).

The numbers are equal ($1 = 1$).

Analysis of Rectangle (Not a Square)

• Lines of Symmetry: Has $2$ lines of symmetry (horizontal and vertical).
• Rotational Symmetry: Order $2$ (rotates $180^\circ$ and $360^\circ$).

The numbers are equal ($2 = 2$).

Analysis of Equilateral Triangle

• Lines of Symmetry: Has $3$ lines of symmetry.
• Rotational Symmetry: Order $3$ (rotates $120^\circ$, $240^\circ$, and $360^\circ$).

The numbers are equal ($3 = 3$).

Analysis of Kite (Not a Square)

• Lines of Symmetry: Has $1$ line of symmetry (main diagonal).
• Rotational Symmetry: Order $1$ (returns to original position only after $360^\circ$ rotation).

The numbers are equal ($1 = 1$).

Conclusion

All plane figures have the same number of lines of symmetry and rotational symmetry order. Therefore, the number of plane figures where the reflectional and rotational symmetries are not equal is $0$.