# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/9

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Question 9

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## Exercise 9

### Question

export const metadata = {
  title: "Question 9",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Consider the following plane figures:
1. Isosceles right triangle.
2. Right trapezoid (not a rectangle).
3. Rectangle (not a square).
4. Rhombus (not a square).

How many figures have the number of rotational symmetries equal to the number of folding symmetries (lines of symmetry)?


### Choices

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

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 9",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

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: <InlineMath math="1" /> (altitude from the right angle to the hypotenuse).
   - Rotational symmetries: <InlineMath math="1" /> (rotation of <InlineMath math="360^\circ" />).
   - **Conclusion**: The numbers are equal.

2. **Right trapezoid**
   - Lines of symmetry: <InlineMath math="0" />.
   - Rotational symmetries: <InlineMath math="1" /> (rotation of <InlineMath math="360^\circ" />).
   - **Conclusion**: The numbers are not equal.

3. **Rectangle** (not a square)
   - Lines of symmetry: <InlineMath math="2" /> (vertical and horizontal axes).
   - Rotational symmetries: <InlineMath math="2" /> (rotation of <InlineMath math="180^\circ" /> and <InlineMath math="360^\circ" />).
   - **Conclusion**: The numbers are equal.

4. **Rhombus** (not a square)
   - Lines of symmetry: <InlineMath math="2" /> (both diagonals).
   - Rotational symmetries: <InlineMath math="2" /> (rotation of <InlineMath math="180^\circ" /> and <InlineMath math="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 <InlineMath math="3" /> figures that satisfy the condition.


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