In `Delta ABC, BD and CE are perpendicular to AC and AB respectively. If `BD = CE`, then `Delta ABC ` is

Options

A. Equilateral
B. Isosceles
C. Right-angled
D. Scalene

Answer

To solve the problem, we need to analyze the given information about triangle ABC and the perpendiculars BD and CE.

### Step-by-Step Solution:

1. **Understand the Triangle Configuration**:
We have triangle ABC, where BD is perpendicular to AC and CE is perpendicular to AB.

2. **Identify the Lengths of the Perpendiculars**:
We are given that BD = CE. This means the heights from points D and E to the respective bases AC and AB are equal.

3. **Use the Property of Triangles**:
In any triangle, if two heights (altitudes) from different vertices to their respective bases are equal, then the bases must also be equal for the triangle to maintain its shape.

4. **Conclusion about the Triangle**:
Since BD = CE and they are the heights from points B and C to sides AC and AB respectively, it follows that the lengths of the bases AC and AB must be equal. Therefore, triangle ABC is an isosceles triangle.

### Final Answer:
Triangle ABC is an **isosceles triangle**.

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