Hong Kong
Stage 1 - Stage 3

Lesson

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

## Some quadrilaterals have specific SIDE properties:

 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

 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.

#### Worked Examples

##### Question 1

ABCD in the adjacent figure is a parallelogram.  Find $x$x and give reasons.

##### Question 2

In kite VRTU:

a) Which pairs of sides are equal?

b) Find the size of $\angle VRU$VRU, give reasons.