RECTANGLE

PRERNA FOR IAS

RECTANGLE

1. Definition of a Rectangle

A rectangle is a four-sided closed figure in which opposite sides are equal and parallel, and all interior angles are 90 degrees. It is one of the most common geometric shapes and is widely used in architecture, engineering, design, and mathematics due to its regular and symmetrical structure.

2. Opposite Sides are Equal

In a rectangle, opposite sides have the same length. If ABCD is a rectangle, then AB = CD and AD = BC. This property ensures balance and symmetry. It is useful for solving geometric problems involving perimeter, area, and side measurements in practical applications.

3. Opposite Sides are Parallel

The opposite sides of a rectangle are parallel to each other. AB is parallel to CD, and AD is parallel to BC. Since parallel lines never intersect, this property helps maintain the rectangular shape and is important in geometry, engineering, and construction designs.

4. All Angles are Right Angles

Every interior angle of a rectangle measures exactly 90 degrees. Therefore, ∠A = ∠B = ∠C = ∠D = 90°. This property distinguishes rectangles from general parallelograms and makes calculations involving area, perimeter, and diagonal lengths easier and more accurate.

5. Diagonals are Equal

The two diagonals of a rectangle have equal lengths. If AC and BD are the diag