Opposite angles in a parallelogram are equal
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 Angles in a rectangle are equal to 90°

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

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

1 pair of opposite parallel sides 
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 )
For each of the shapes below, choose the most precise classification.
Trapezium
Rectangle
Square
Trapezium
Rectangle
Square
Square
Trapezium
Rectangle
Square
Trapezium
Rectangle
Trapezium
Rectangle
Square
Trapezium
Rectangle
Square
Trapezium
Rectangle
Square
Trapezium
Rectangle
Square
Trapezium
Square
Rectangle
Trapezium
Square
Rectangle
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:
Rhombus
Square
Trapezium
Rectangle
Rhombus
Square
Trapezium
Rectangle
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.
A summary of the geometrical properties of angles can be found here.
A summary of the geometrical properties of triangles can be found here.