The type of quadrilateral that is not always a parallelogram is a rhombus. Here's why:
1. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. It has the following properties:
- Opposite sides are parallel.
- Opposite sides are equal in length.
- Opposite angles are equal.
- Consecutive angles are supplementary.
2. A rhombus is a type of quadrilateral where all four sides are equal in length, but it does not necessarily have opposite sides that are parallel. The properties of a rhombus are:
- All sides are equal in length.
- Opposite angles are equal.
- Diagonals bisect each other at right angles.
3. While a rhombus can have its opposite angles equal and diagonals that bisect each other at right angles, it does not guarantee that its opposite sides are parallel. Therefore, a rhombus is not always a parallelogram because it lacks the requirement of having opposite sides that are both parallel and equal in length.
In summary, a rhombus is a quadrilateral that is not always a parallelogram due to the specific properties it possesses, such as equal side lengths without the necessity of having parallel opposite sides.
