Some Special Parallelograms
This section delves into the properties and definitions of special types of parallelograms, namely the rhombus, rectangle, and square. A rhombus is defined as a quadrilateral with all sides equal in length; it shares properties with both parallelograms and kites. A distinct property of a rhombus is that its diagonals are perpendicular bisectors of one another, emphasizing their unique geometric relationship.
Next, we explore rectangles which are parallelograms featuring equal angles, specifically, each angle measures 90 degrees. We establish that all rectangles have opposite sides of equal length and their diagonals are congruent. The proof involves using the triangles formed by diagonal cuts demonstrating the properties of parallelograms.
Finally, the square is defined as a special case of both a rectangle and a rhombus, possessing all the properties encapsulated by both definitions. Importantly, the diagonals of a square not only bisect each other but are also perpendicular bisectors. This highlights the square’s unique characteristics among quadrilaterals.