all 4 interior angles of a parallelogram which is not a rectangle are bisected.What shape is always enclosed by the 4 bisectors
To determine what shape is always enclosed by the four bisectors of the interior angles of a parallelogram (which is not a rectangle), let's break down the problem step by step.
Step 1: Understand the problem.
A parallelogram is a quadrilateral with opposite sides that are parallel. However, since it is stated that the parallelogram is not a rectangle, we know that its interior angles are not right angles (90 degrees).
Step 2: Recognize that four bisectors create a smaller shape.
When the four interior angles of a parallelogram are bisected, the bisectors divide each angle into two equal angles. This means that each of the original four angles is divided into two smaller angles.
Step 3: Determine the shape formed.
By bisecting the interior angles of the parallelogram, we end up with eight smaller angles. These smaller angles are congruent (equal in measure) due to the bisectors. When we draw lines connecting the bisectors' endpoints, they enclose a new shape.
Step 4: Identify the shape.
The shape that is always enclosed by the four bisectors of the interior angles of a parallelogram (which is not a rectangle) is a rectangle. The reason is that the four bisectors will intersect at right angles, creating sides that are perpendicular to each other.
To recap, the four bisectors of the interior angles of a parallelogram (which is not a rectangle) will always form a rectangle.