First of all, every rectangle is a parallelogram but a parallelogram is not a rectangle. When you see the properties of a rectangle and parallelogram, they are almost the same. Some of the common properties of both the 2-dimensional figures are
- Both are quadrilaterals
- Opposite sides are parallel to each other
- Adjacent angles are supplementary
- Diagonals bisect each other
- Opposite sides are of equal length.
The differences between rectangle and parallelogram are like all the angles of a rectangle are of 900 whereas the angles of a parallelogram can differ. Another dissimilarity is; diagonal length is equal in a rectangle but it is not the same for a parallelogram.
When you consider both the quadrilaterals, area of a rectangle is equal to the area of parallelogram because both have the same length and breadth and the area of both quadrilaterals is defined by the product of length and breadth. However, the perimeter of rectangle and parallelogram remains the same. From the property, you can say the perimeter of quadrilaterals having equal lengths on opposite sides. All the requirements of the parallelogram are applied to a rectangle because a rectangle is a subset of a parallelogram. So that every rectangle can be a parallelogram but the reverse process is not possible. Only a few parallelograms are rectangles if and only if its angle becomes 900 and the base of both quadrilaterals remains the same.
Also, it can be stated that all the parallelograms are the flexible rectangles such that they have the combination of angles with 2 duplicate pair of angles which equals to 3600 whereas the rectangles are the inflexible parallelograms with 4 duplicate angles. The hierarchy behind this is every rectangle is a parallelogram and every parallelogram is a quadrilateral. But you cannot say that every quadrilateral is a parallelogram and every parallelogram is a rectangle.
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