The number of lines of symmetry which a triangle cannot have is

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine the number of lines of symmetry that a triangle cannot have, we will analyze the different types of triangles and their properties regarding symmetry.

### Step-by-Step Solution:

1. **Understand the Types of Triangles**:
- There are three main types of triangles:
- Equilateral Triangle
- Isosceles Triangle
- Scalene Triangle

2. **Identify the Lines of Symmetry for Each Type**:
- **Equilateral Triangle**:
- All three sides are equal.
- It has **3 lines of symmetry**. Each line can be drawn from a vertex to the midpoint of the opposite side.
- **Isosceles Triangle**:
- Two sides are equal.
- It has **1 line of symmetry**. This line can be drawn from the vertex angle to the midpoint of the base.
- **Scalene Triangle**:
- All sides are of different lengths.
- It has **0 lines of symmetry**. There are no equal sides or angles to create a line of symmetry.

3. **Analyze the Options Given**:
- The options provided are:
- 0
- 1
- 2
- 3
- We need to find the number of lines of symmetry that a triangle cannot have.

4. **Determine Which Option is Correct**:
- From our analysis:
- An equilateral triangle can have 3 lines of symmetry.
- An isosceles triangle can have 1 line of symmetry.
- A scalene triangle cannot have any lines of symmetry (0).
- The only number of lines of symmetry that a triangle cannot have is **2**.

### Conclusion:
The number of lines of symmetry which a triangle cannot have is **2**.

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