NZ Level 4
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Types of Quadrilaterals
Lesson

Identifying Geometric Shapes by their properties

Parallelogram

Opposite angles in a parallelogram are equal

 

Opposite sides in a parallelogram are parallel

 

Opposite sides in a parallelogram are equal

 


Rectangle

Opposite sides in a rectangle are parallel

 

Opposite sides in a rectangle are equal

 

Angles in a rectangle are equal to 90° 

 


Square

All angles in a square are equal to 90° 

 

All sides of a square are equal

 

Opposite sides in a square are parallel

 

 

RHombus

Opposite sides in a rhombus are parallel

 

Opposite angles of a rhombus are equal

 

All sides of a rhombus are equal

 

 

Trapezium

1 pair of opposite parallel sides

 

Kite

2 pairs of equal adjacent sides

 

1 pair of opposite equal angles

 

 

 

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 -)

Worked Examples

Question 1

For each of the shapes below, choose the most precise classification.

  1. Trapezium

    A

    Rectangle

    B

    Square

    C

    Trapezium

    A

    Rectangle

    B

    Square

    C
  2. Square

    A

    Trapezium

    B

    Rectangle

    C

    Square

    A

    Trapezium

    B

    Rectangle

    C
  3. Trapezium

    A

    Rectangle

    B

    Square

    C

    Trapezium

    A

    Rectangle

    B

    Square

    C
  4. Trapezium

    A

    Rectangle

    B

    Square

    C

    Trapezium

    A

    Rectangle

    B

    Square

    C
  5. Trapezium

    A

    Square

    B

    Rectangle

    C

    Trapezium

    A

    Square

    B

    Rectangle

    C

 

Question 2

Patricia draws a quadrilateral, and covers it up. She tells Glen that the quadrilateral consists of right angles only. From this information, Glen knows that the quadrilateral is definitely a:

  1. Rhombus

    A

    Square

    B

    Trapezium

    C

    Rectangle

    D

    Rhombus

    A

    Square

    B

    Trapezium

    C

    Rectangle

    D

 

Solving problems

When solving angle problems in geometry one of the most important components is the reasoning (or rules) you use to solve the problem.  You will mostly be required in geometry problems to not only complete the mathematics associated with calculating angle or side lengths but also to state the reasons you have used.  Read through each of these rules and see if you can describe why and draw a picture to represent it.

Properties of quadrilaterals

Parallelogram

  • Opposite sides in a parallelogram are parallel
  • Opposite angles in a parallelogram are equal
  • Opposite sides in a parallelogram are equal

 

 

Rectangle

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

 

 

Square

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

 

 

Rhombus

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

 

 

Trapezium

  • An isosceles trapezium (trapezoid) has 2 pairs of adjacent angles equal
  • A trapezium (trapezoid) has one pair of opposite sides parallel
  • An isosceles trapezium (trapezoid) has one pair of opposites sides equal

 

 

Kite

  • A kite has 2 pairs of adjacent sides equal
  • A kite has 1 pair of opposite angles equal

 

 

A summary of the geometrical properties of angles can be found here.  

A summary of the geometrical properties of triangles can be found here. 

Outcomes

GM4-5

Identify classes of two- and threedimensional shapes by their geometric properties

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