**Answer:**

To construct a triangle, we need to have certain information about the triangle. Among the options given, the correct answer is option 'A' - the lengths of the three sides.

**Reasoning:**

To construct a triangle, we need to have the following information:

1. **Lengths of the three sides:** The lengths of the three sides of the triangle determine the shape and size of the triangle. By knowing the lengths of the three sides, we can determine the type of triangle, whether it is equilateral, isosceles, or scalene. For example, if all three sides are equal in length, then it is an equilateral triangle. If two sides are equal in length, then it is an isosceles triangle. If all three sides have different lengths, then it is a scalene triangle.

2. **Perimeter of the triangle:** The perimeter of a triangle is the sum of the lengths of its three sides. While the perimeter provides information about the total distance around the triangle, it does not give us enough information to construct the triangle accurately. Different combinations of side lengths can result in different shapes and sizes of triangles, so knowing only the perimeter is not sufficient to construct a unique triangle.

3. **Measures of three angles:** The measures of the three angles of a triangle determine the shape and type of the triangle. However, knowing only the measures of the three angles is not sufficient to construct a unique triangle. Multiple triangles can have the same set of angle measures but different side lengths, resulting in different shapes and sizes.

4. **Names of three vertices:** The names of the three vertices of a triangle simply indicate the position or location of the triangle's corners. They do not provide any information about the lengths of the sides or the measures of the angles, which are essential to construct a triangle accurately.

Therefore, among the given options, the lengths of the three sides (option 'A') are necessary and sufficient information to construct a triangle.

As triangle have three sides and a polygon.
Polygon is a closed figure with at least three sides.
As we know three sides is needed as well as closed figure.
Therefore, Side is needed for closed figure.
So the answer is (A)