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.