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Stage 1 - Stage 3

Angles and Lengths in Quadrilaterals Revision

Lesson

All quadrilaterals

  • Sum of exterior angles of a polygon is $360$360°
  • Angle sum of a quadrilateral is $360$360°

 

Parallelogram

Opposite angles in a parallelogram are equal

 

Opposite sides in a parallelogram are parallel

 

Opposite sides in a parallelogram are equal

 

Diagonals of a parallelogram bisect each other $BO=DO$BO=DO and $AO=CO$AO=CO)

 

Rectangle

Opposite sides in a rectangle are equalOpposite sides in a rectangle are parallel

 

Angles in a rectangle are equal to 90° 

 

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)

 

Square

All sides of a square are equalAll angles in a square are equal to 90° 

 

Opposite sides in a square are parallel

 

Diagonals of a square are perpendicular to each other (cross at 90°)

 

Diagonals of a square bisect the angles at the vertices (makes them 45°)

 

Diagonals of a square bisect each other ($BO=DO$BO=DO$AO=CO$AO=CO )

 

Diagonals of a square are equal ($AC=BD$AC=BD)

 

Rhombus

Opposite angles of a rhombus are equalOpposite sides in a rhombus are parallel

 

All sides of a rhombus are equal

 

Diagonals of a rhombus bisect each other at 90 degrees ($BO=DO$BO=DO and$AO=CO$AO=CO)

 

Diagonals of a rhombus bisect corner angles. i.e. $\angle OAB=\angle OAD$OAB=OAD,  $\angle OCD=\angle OCB$OCD=OCB,  $\angle OBC=\angle OBA$OBC=OBA and $\angle ODC=\angle ODA$ODC=ODA

 

Diagonals of a rhombus bisect each other   ($BO=DO$BO=DO and $AO=CO$AO=CO)

 

Kite

1 pair of opposite equal angles2 pairs of equal adjacent sides

 

The longest diagonal of a kite bisects the angles through which it passes. i.e. $\angle BAO=\angle DAO$BAO=DAO and $\angle COD=\angle COB$COD=COB 

 

Diagonals of a kite are perpendicular to each other.

 

The longest diagonal of a kite bisects the shorter diagonal ($BO=OD$BO=OD)

 

Trapezium

>1 pair of opposite parallel sides

 

Isosceles Trapezium

Diagonals of an isosceles trapezium (trapezoid) are equal ($DB=AC$DB=AC)1 pair of opposite parallel sides

 

 

 

 

Now that you know about 6 different types of quadrilaterals. Move the points (vertices) around and see how many different quadrilaterals you can find in the interactive below.  (Watch this video if you would like to see this interactive in action -)

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

Calculate $x$x giving reasons.

Question 2

Question 3

Find the value of all pronumerals in the figure, giving reasons.