Certain quadrilaterals are recognized as special parallelograms due to their unique properties. These include:

1. Rhombus
2. Rectangle
3. Square

Let’s explore each of these in detail:

1. Rhombus

Definition: A rhombus is a parallelogram where all four sides are of equal length.

Properties:

• Equal Sides: All sides have the same length.
• Opposite Angles: Equal in measure.
• Diagonals:
  • Bisect each other at right angles (90°).
  • Divide the rhombus into four right-angled triangles.

2. Rectangle

Definition: A rectangle is a parallelogram with each angle measuring 90°.

Properties:

• Equal Opposite Sides: Opposite sides are equal and parallel.
• All Angles: Each angle is a right angle (90°).
• Diagonals:
  • Equal in length.
  • Bisect each other.

3. Square

Definition: A square is a parallelogram with all sides equal and all angles measuring 90°.

Properties:

• Equal Sides: All four sides are of equal length.
• All Angles: Each angle is a right angle (90°).
• Diagonals:
  • Equal in length.
  • Bisect each other at right angles (90°).
  • Divide the square into four right-angled isosceles triangles.

Key Takeaways:

• A rhombus has all sides equal, diagonals that bisect each other at right angles, and equal opposite angles.
• A rectangle has equal opposite sides, all angles equal to 90°, and equal diagonals that bisect each other.
• A square combines the properties of both a rhombus and a rectangle, with all sides equal, all angles equal to 90°, and equal diagonals that bisect each other at right angles.