# 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.

#### 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.