Draw and list the properties of a kite, trapezium, parallelogram, and rhombus.

Here are the drawings and properties for each quadrilateral:

1. Kite

   • Drawing: Imagine a shape with four vertices. Connect two pairs of adjacent sides so that each pair has equal length. For example, if the vertices are A, B, C, D in order, then AB = AD and CB = CD. The shape will look like a traditional kite.
   • Properties:
     • Two distinct pairs of adjacent sides are equal in length.
     • One pair of opposite angles are equal.
     • The diagonals are perpendicular to each other.
     • One diagonal bisects the other diagonal.
     • One diagonal bisects the angles at the vertices it connects.

2. Trapezium (also known as Trapezoid)

   • Drawing: Draw a quadrilateral where only one pair of opposite sides are parallel. The other two sides are not parallel.
   • Properties:
     • Exactly one pair of opposite sides are parallel.

3. Parallelogram

   • Drawing: Draw a quadrilateral where both pairs of opposite sides are parallel. It looks like a "slanted" rectangle.
   • Properties:
     • Opposite sides are parallel.
     • Opposite sides are equal in length.
     • Opposite angles are equal.
     • Consecutive angles are supplementary (add up to $180^\circ$).
     • The diagonals bisect each other.

4. Rhombus

   • Drawing: Draw a parallelogram where all four sides are equal in length. It looks like a "slanted" square.
   • Properties:
     • All four sides are equal in length.
     • Opposite sides are parallel.
     • Opposite angles are equal.
     • The diagonals bisect each other at right angles ($90^\circ$).
     • The diagonals bisect the angles at the vertices.

5. Rectangle

   • Drawing: Draw a parallelogram where all four angles are right angles ($90^\circ$).
   • Properties:
     • All four angles are right angles ($90^\circ$).
     • Opposite sides are parallel and equal in length.
     • The diagonals are equal in length.
     • The diagonals bisect each other.