The ans is option d the bisectors of the angles of a parallelogram enclose a rectangle .

Bisectors of the angles of a parallelogram enclose a rectangle.

Explanation:

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal.

When we draw the bisectors of the angles of a parallelogram, we divide each angle into two equal parts.

Proof:

Let's consider a parallelogram ABCD.

1. Draw the bisector of angle A:
- Draw a line that passes through the vertex A and divides angle A into two equal parts. Let this line intersect the opposite side DC at point E.

2. Draw the bisector of angle B:
- Draw a line that passes through the vertex B and divides angle B into two equal parts. Let this line intersect the opposite side AD at point F.

3. Draw the bisector of angle C:
- Draw a line that passes through the vertex C and divides angle C into two equal parts. Let this line intersect the opposite side AB at point G.

4. Draw the bisector of angle D:
- Draw a line that passes through the vertex D and divides angle D into two equal parts. Let this line intersect the opposite side BC at point H.

Properties of the bisectors:

- The bisector of angle A divides the opposite side DC into two equal parts, DE and EC.
- The bisector of angle B divides the opposite side AD into two equal parts, AF and FD.
- The bisector of angle C divides the opposite side AB into two equal parts, AG and GB.
- The bisector of angle D divides the opposite side BC into two equal parts, BH and HC.

Analysis:

By drawing the bisectors of the angles of the parallelogram, we can observe the following:

- The bisectors of angles A and C are parallel to each other, as are the bisectors of angles B and D.
- The bisectors of angles A and C intersect at point G, and the bisectors of angles B and D intersect at point F.
- The bisectors of angles A and D intersect at point E, and the bisectors of angles B and C intersect at point H.

Conclusion:

From the properties and analysis, we can conclude that the bisectors of the angles of a parallelogram enclose a rectangle. In a rectangle, opposite sides are parallel and equal in length, and all angles are right angles. Therefore, the correct answer is option 'D' - Rectangle.