Special Parallelograms: Rhombus, Square & Rectangle

Before talking about the special parallelograms, let us recall what a parallelogram is. A parallelogram is a quadrilateral with two pairs of parallel sides.  The opposite sides are parallel and equal in length. The opposite angles are equal in measure. The adjacent angles are supplementary and it has 2 diagonals that bisect each other. In this article, we will discuss some special parallelograms – rhombus, rectangle and square.

Rhombus

A rhombus is a quadrilateral with all the four sides having equal lengths.

Rhombus

  • In a rhombus, the opposite sides are parallel and equal. Hence, it is a parallelogram.
  • However, all the 4 sides are equal in a rhombus.
  • Opposite angles are equal.
  • Diagonals of a rhombus intersect each other at right angles.
  • Diagonals bisect each other.
  • Diagonals bisect opposite vertex angles.
  • Each of the diagonal divides the rhombus into 2 congruent triangles.

Rectangle

A rectangle is a parallelogram with all the 4 angles having equal measure.

Rectangle

  • Opposite sides are equal in length.
  • Opposite sides are parallel.
  • The interior angles measure 90 degrees each.
  • Diagonals are equal in length.
  • Diagonals bisect each other.
  • Each of the diagonal bisects the rectangle into 2 congruent triangles.
  • It has 2 lines of symmetry – a horizontal and a vertical.
  • The mid-points of the 4 sides of a rectangle, when joined in order, form a rhombus.

Square

A square is a rectangle with equal sides.

Square

  • All the 4 sides are equal in length.
  • Opposite sides are parallel.
  • The interior angles measure 90 degrees each.
  • Diagonals are equal in length.
  • Diagonals bisect each other at right angles.
  • Diagonals bisect opposite vertex angles.
  • It is a highly symmetric figure with 4 lines of symmetry – a horizontal, a vertical and the 2 diagonals.
  • Each of the diagonal bisects the square into 2 congruent triangles. In fact, both the pairs of congruent triangles are also congruent to one another.

Practise This Question

X1234Y10203040
What would be the constant that defines the value XY ?