As we have seen in Types of Quadrilaterals there are specific geometric properties relating to sides and angles that explicitly define certain shapes.
Opposite sides in a parallelogram are parallel
Opposite sides in a parallelogram are equal


Opposite sides in a rectangle are parallel
Opposite sides in a rectangle are equal


All sides of a square are equal
Opposite sides in a square are parallel


Opposite sides in a rhombus are parallel
All sides of a rhombus are equal


1 pair of opposite parallel sides  
An isosceles trapezium (trapezoid) has one pair of opposite sides equal
One pair of opposite parallel sides


2 pairs of equal adjacent sides 
In addition to the properties already studied, the diagonals of some quadrilaterals also have special properties.
Diagonals of a parallelogram bisect each other ($BO=DO$BO=DO &$AO=CO$AO=CO)  
Diagonals of a rectangle bisect each other ($BO=AO$BO=AO= $DO=CO$DO=CO )
Diagonals in a rectangle are equal ($BD=CA$BD=CA)


Diagonals of a square are equal ($AC=BD$AC=BD)
Diagonals of a square bisect each other ($BO=DO$BO=DO = $AO=CO$AO=CO )


Diagonals of a rhombus bisect each other ($BO=DO$BO=DO and $AO=CO$AO=CO)  
The longest diagonal of a kite bisects the shorter diagonal ($BO=OD$BO=OD)  
Diagonals of an isosceles trapezium (trapezoid) are equal ($DB=AC$DB=AC) 
The following applet will allow you to manipulate different quadrilaterals using the blue points and see the properties appear with regards to the diagonals.
ABCD in the adjacent figure is a parallelogram. Find $x$x and give reasons.
In kite VRTU:
a) Which pairs of sides are equal?
b) Find the size of $\angle VRU$∠VRU, give reasons.
Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties