Let A,B,C,D be four points in a plane such that no three of them are collinear and the line segments AB,BC,CD,DA do not intersect except at their end points . Then the figure formed by these four line segments is called the Quadrilateral ABCD.

In the quadrilateral ABCD :

1>the four points ABCD are called its vertices 2>the four line segments AB, BC, CD, DA are called its sides 3> /_DAB /_ABC/_BCD/_CDA are called its angles 4>the line segments AC and BD are called its diagonals

There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and

the sum of their four interior angles equals 360 degrees.

TYPES OF QUADRILATERALS

CONVEX QUADRLATERAL - a quadrilateral in which the measure of each angle is less than 180 .

CONCAVE QUADRILATERAL- - A quadrilateral in which the measure of at least one of the angles is more than 180 .

The sum of the angles of a quadrilateral is 360 or 4 right angles . PROOF: Let ABCD be any quadrilateral Draw one of its diagonals AC. Clearly we have :/_A =/_1 + /_2 and /_C= /_3 +/_4. We know that the sum of the angles of a triangle is 180 . Therefore in ABC we have /_2+/_4+/_B = 180 and in ACD we have /_1+/_D+/_3=180 . Adding the angles on either side we get: /_1+/_2+/_3+/_4+/_D+/_B+ = 360

If the sides of a quadrilateral are produced in an order , the sum of the 4 exterior angles so formed is 360 . Proof : Let the sides of a quadrilateral ABCD be produced in an order forming exterior angles /_1,/_2/_3,/_4 . We know that the sum of the angles of an linear pair is 180 . Therefore /_1+/_A=180 , /_2+/_B=180 ,/_3+/_C=180, /_4+/_D=180. Adding the angles on either side we get 720 . But /_A+/_B+/_+C+/_D=360 therefore /_1+/_2+/_3+/_4=360

Quadrilaterals are called parallelograms if both pairs of opposite sides are equal

and parallel to each other.  Different parallelograms and their properties are

described below.

Parallelogram

•Opposite sides of a parallelogram are parallel and equal in length.

•Opposite angles are equal in size.

                                           

                                                                              

A rectangle is a four-sided shape where every angle is a right angle (90°). Also opposite sides are parallel and of equal length

*RectangleI have all of the properties of the parallelogram PLUS

- 4 right angles- diagonals congruent

A rhombus is a four-sided shape where all sides have equal

length.

Also opposite sides are parallel and opposite angles are equal.Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus

bisect each other at right angles.

*RhombusI have all of the properties of

the parallelogram PLUS- 4 congruent sides

- diagonals bisect angles- diagonals perpendicular

A square has equal sides and every angle is a right angle (90°)

Also opposite sides are parallel.

*SquareHey, look at me!

I have all of the properties of the parallelogram A

ND the rectangle AND the rhombus.

I have it all!

Trapezium

•A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the diagram.

                                     •A trapezium has one pair of opposite sides parallel.

*TrapezoidI have only one set of

parallel sides. [The median of a trapezoid is parallel to the bases and equal to one-half the sum

of the bases.]

•Two pairs of adjacent sides of a kite are equal in length •One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size. •One diagonal bisects the other. •Diagonals intersect at right angles.