Quadrilateral with all sides equal and one side at 90 degrees: Rhombus

A quadrilateral is a polygon with four sides. There are various types of quadrilaterals, each with its own unique characteristics. One type of quadrilateral that fits the given criteria of having all sides equal and one side at 90 degrees is a rhombus.

Definition of a Rhombus:
A rhombus is a quadrilateral with all sides equal in length. It is also known as a diamond-shaped figure. In a rhombus, opposite sides are parallel and opposite angles are equal. Additionally, the diagonal of a rhombus bisects each other at a right angle.

Characteristics of a Rhombus:
1. Equal sides: All sides of a rhombus are of equal length. This means that the length of AB is equal to BC, CD, and DA, where A, B, C, and D are the vertices of the rhombus.
2. Opposite sides parallel: The opposite sides of a rhombus are parallel. This means that side AB is parallel to side CD, and side BC is parallel to side DA.
3. Opposite angles equal: The opposite angles of a rhombus are equal. This means that angle A is equal to angle C, and angle B is equal to angle D.
4. Diagonals bisect each other at right angles: The diagonals of a rhombus bisect each other at right angles. This means that the line segment connecting the midpoints of AC and BD is perpendicular to both AC and BD.
5. One right angle: A rhombus has one angle that measures 90 degrees. This occurs where the diagonals intersect.

Example:
To visualize a rhombus, imagine a square tilted to the side. All the sides of a rhombus have the same length, and one of its angles is a right angle. The diagonals of a rhombus are not equal in length, but they bisect each other at right angles.

In conclusion, a rhombus is a quadrilateral that has all sides equal in length and one angle measuring 90 degrees. It possesses unique properties such as opposite sides being parallel, opposite angles being equal, and diagonals bisecting each other at right angles.