Quadrilaterals are named according to their properties and are as follows:
A parallelogram has opposite sides which are equal and parallel. The diagonals of a parallelogram bisect each other and it has a rotational symmetry of order 2.
A rhombus is a parallelogram but with four equal sides. The diagonals of a rhombus beset each other at right angles, it has a two line symmetry and a rotational symmetry of two.
A rectangle has opposite sites of equal length and has four right angles. It also has two lines of symmetry and a rotational symmetry order of two.
A square has four equal sides and four right angles. It also has four lines of symmetry and a rotational symmetry order of 4.
A trapezium has one pair of opposite sides that are parallel. It also has one line of symmetry but no rotational symmetry.
In an isosceles trapezium the two opposite non-parallel sides are the same length. It also has diagonals of the same length but with only one line of symmetry.
A kite has two pairs of adjacent sides of equal length. The diagonals of a kite cross at right angles and it only has one line of symmetry.
An arrowhead or delta has two pairs of adjacent sides of equal length and one interior angle that is more than 180°. The diagonals cross at right angles outside the shape and has only one line of symmetry.