# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/18

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 18

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## Exercise 18

### Question

export const metadata = {
  title: "Problem 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Given <InlineMath math="4" /> plane figures as follows:

1. Isosceles trapezoid.
2. Rectangle (not a square).
3. Equilateral triangle.
4. Kite (not a square).

How many plane figures have a number of lines of symmetry that is not equal to their order of rotational symmetry?


### Choices

- [x] $$0$$
- [ ] $$1$$
- [ ] $$2$$
- [ ] $$3$$
- [ ] $$4$$

### Answer & Explanation

export const metadata = {
  title: "Explanation for Problem 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

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 <InlineMath math="1" /> line of symmetry (vertical line in the middle).
- **Rotational Symmetry**: Order <InlineMath math="1" /> (returns to original position only after <InlineMath math="360^\circ" /> rotation).

The numbers are equal (<InlineMath math="1 = 1" />).

#### Analysis of Rectangle (Not a Square)

- **Lines of Symmetry**: Has <InlineMath math="2" /> lines of symmetry (horizontal and vertical).
- **Rotational Symmetry**: Order <InlineMath math="2" /> (rotates <InlineMath math="180^\circ" /> and <InlineMath math="360^\circ" />).

The numbers are equal (<InlineMath math="2 = 2" />).

#### Analysis of Equilateral Triangle

- **Lines of Symmetry**: Has <InlineMath math="3" /> lines of symmetry.
- **Rotational Symmetry**: Order <InlineMath math="3" /> (rotates <InlineMath math="120^\circ" />, <InlineMath math="240^\circ" />, and <InlineMath math="360^\circ" />).

The numbers are equal (<InlineMath math="3 = 3" />).

#### Analysis of Kite (Not a Square)

- **Lines of Symmetry**: Has <InlineMath math="1" /> line of symmetry (main diagonal).
- **Rotational Symmetry**: Order <InlineMath math="1" /> (returns to original position only after <InlineMath math="360^\circ" /> rotation).

The numbers are equal (<InlineMath math="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 <InlineMath math="0" />.


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