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A quadrangle is a polygon with four (quad-) angles (and four sides). They can also be called quadrilaterals. As you can see below, there are many different types of quadrangles.

We can use three different shape aspects to classify quadrangles:

• side lengths,
• side orientations, and
• angle sizes.
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We can also use axes of symmetry to help identify them. Unlike triangles however, we generally need to look at a combination of the above to correctly distinguish one quadrangle from another (as you'll see below). Hint: Mouse over the images below to help you compare shapes' properties.

There are three steps involved in classifying a quadrangle:
○ Identify and count parallel sides;
○ Identify and count any sides of equal length; and
○ Compare the internal angles.

Two sets of parallel sides
Shapes with two sets of parallel sides include the parallelogram, rhombus, square, and rectangle. Due to the nature of being four-sided shapes with two sets of parallel sides, these shapes will all have two axes of symmetry. To correctly identify each one, we need to study their angles and the length of their sides.

Two sets of equal opposite angles ≠ 90 degrees
~ If two pairs of opposing sides are equal length = parallelogram
~ If all four sides are equal = rhombus

*NB: Strictly speaking, rhombi can have angles = 90 degrees; we just call these special types of rhombi squares (see below).

All angles = 90 degrees
~ If two pairs of opposing sides are equal length = rectangle or oblong
~ If all four sides are equal = square

Only one set of parallel sides
This shape is a trapezoid, or also known as a trapezium. As you can see in the image below, trapezoids come in an assortment of angles and sides; what is common among them all is the one set of parallel sides.

No parallel sides
If there are two pairs of adjacent sides of equal length (i.e. one set of opposite angles of equal value) then the shape is a kite. You'll note below that kites also have an axis of symmetry.
~ If it has one angle >180 degrees, the kite is concave
~ If all angles are < 180 degrees, the kite is convex
*NB: Remember, an angle can't = 180 degrees in a shape - it would just become one continuous side if it was.

If there are no sides of equal length or parallel in orientation, the shape is known as a irregular polygon / quadrangle.