In `triangle ABC`, `AB=AC` and `AD bot BC,BE bot AC` and `CF bot AB`. Then `triangle ABC` is symmetrical about

Options

A. AD
B. BE
C. CF
D. None of these

Answer

To solve the problem, we need to determine the line of symmetry in triangle ABC, given that AB = AC and certain perpendiculars are drawn from points A, B, and C to the opposite sides.

### Step-by-Step Solution:

1. **Identify the Triangle**:
We start by drawing triangle ABC where AB = AC. This means triangle ABC is an isosceles triangle.

**Hint**: Remember that in an isosceles triangle, two sides are equal.

2. **Draw the Perpendiculars**:
We are given that:
- AD is perpendicular to BC
- BE is perpendicular to AC
- CF is perpendicular to AB

We will draw these perpendiculars accordingly.

**Hint**: Perpendiculars form right angles (90 degrees) with the sides they intersect.

3. **Analyze the Symmetry**:
In an isosceles triangle, the line of symmetry is the perpendicular drawn from the vertex angle (A in this case) to the base (BC). This line divides the triangle into two equal halves.

**Hint**: The line of symmetry in an isosceles triangle always passes through the vertex opposite the base.

4. **Conclusion**:
Since AD is the perpendicular from A to BC, it acts as the line of symmetry for triangle ABC. Therefore, triangle ABC is symmetrical about line AD.

**Hint**: When identifying the line of symmetry, look for the line that divides the triangle into two congruent parts.

### Final Answer:
Triangle ABC is symmetrical about line AD.