12-07-2013, 04:35 PM
Types of Quadrilateral
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A Quadrilateral is a polygon with four sides (or edges) and four vertices or corners.
Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for
consistency with pentagon (5-sided), hexagon (6-sided) and so on. The origin of the word
"quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."
Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called
crossed. Simple quadrilaterals are either convex or concave. The interior angles of a simple
quadrilateral ABCD add up to 360 degrees of arc, that is, This is a special case of the n-gon
interior angle sum formula (n − 2) × 180°.
In a crossed quadrilateral, the interior angles on either side of the crossing add up to 720°. If
all the sides of the quadrilaterals are equal, then we call it the regular quadrilateral. A square
and a rhombus are both regular quadrilaterals. Now we look at the difference of the square and
the Rhombus. Both the above mentioned figures are regular quadrilaterals, but the basic
difference which we can state in one sentence between a square and the rhombus is that the
rhombus is a tilted square.
Thus we conclude that the square has all the four sides equal. On other hand we see that the
opposite angles of the rhombus are equal, but all the angles are not of 90 degrees. In both the
figures we have their diagonals bisecting at 90 degrees, but the diagonals of the rhombus are
not equal, on another hand the diagonals of the square are equal and they are perpendicular
bisector of each other. Now we talk about other quadrilateral, which is a parallelogram. In a
parallelogram, we have opposite sides equal and parallel too. So we say that a square or a
rectangle or a rhombus all the three quadrilaterals are parallelograms as they have opposite
sides equal and parallel. But it is not necessary that all the parallelograms are not squares or
rectangles.
Another important quality of the parallelograms is that their pair of adjacent angles forms a
supplementary pair, and the opposite angles of the parallelogram are equal. Now we come to
another quadrilateral say trapezium. We say that the trapezium is a figure which has one pair
of opposite side’s parallel but not necessary equal. So another pair of the trapezium is neither
equal (necessary) nor parallel. If another pair of the lines of the trapezium is equal, then we
call it an isosceles trapezium. Let us take another figure say kite; a kite has adjacent pair of the
lines as equal, so it has a vertical line of symmetry. Now comes another quadrilateral, irregular
quadrilateral.
It means that all the sided of the given quadrilateral are of different measurement. Square has
four lines of symmetry which are the lines formed by joining mid points of its opposite sides
and the lines formed by joining the diagonals. On other hand a rectangle only has two lines of
symmetry, which are the lines formed by joining the mid points of the opposite sides. We must
remember that a parallelogram and irregular quadrilaterals have no line of symmetry. If we
look at the line of symmetry of the kite, it has no horizontal line of symmetry, but has only one
line of symmetry, which is vertical.