Classify a quadrilateral by its geometric properties
Geometry
A quadrilateral is any four sided shape. The strange, long name comes from Latin: Quad, meaning four, and Lateral, meaning side (fourside).
There are 6 different types of quadrilateral:
Square
 4 equal length sides
 4 right angles
 2 pairs of parallel sides
Rhombus
 4 equal length sides
 2 pairs of equal opposite angles
 2 pairs of parallel sides
Parallelogram
 2 pairs of equal opposite angles
 2 pairs of parallel sides
Trapezium
 1 pair of parallel sides
 a regular trapezium has 2 pairs of adjacent equal angles (that are not right angles)
Kite
 no parallel sides
 2 pairs of adjacent equal length sides
 the angles at which these pairs meet are equal and opposite
 diagonals meet at a right angle and bisect the opposite vertice
Irregular Quadrilateral
 do not fit in any of the above!
Notice: A square is a special type of rhombus, a rhombus is a special type of parallelogram!
Important: ‘Diamond’ is *not* a mathematical name. What people call a diamond is either just a square rotated by 45 degrees, or a rhombus. In primary school, a rectangle will have sometimes been referred to as an oblong. A rectangle *can* be a square (i.e. all squares are also rectangles), whereas an oblong is specifically a rectangle with only two lengths the same i.e. not a square. Oblongs are rarely mentioned at secondary school level.
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