Introduction
We have studied many properties of a triangle in previous chapters, and we know that on joining three non-collinear points in pairs, the figure so obtained is a triangle. Now, let us mark four points and see what we obtain on joining them in pairs in some order.
The above figure shows that,
- If all the points are collinear (in the same line), we obtain a line segment. [see Fig. 1]
- If three out of four points are collinear, we get a triangle. [see Fig. 2]
- If all the points are non-collinear, we obtain a closed figure with four sides .Such a figure formed by joining four points in an order is called a quadrilateral. [see Fig 3 & 4]
In this chapter, we will consider only quadrilaterals of the type given in Fig. 3 but not as given in Fig. 4.
A quadrilateral has
- Four vertices
- Four sides
- Four angles
- Two diagonals
Fig. 8.2
136 MATHEMATICS
In quadrilateral ABCD, AB, BC, CD and DA are the four sides; A, B, C and D are
the four vertices and ∠ A, ∠ B, ∠ C and ∠ D are the four angles formed at the
vertices.
Now join the opposite vertices A to C and B to D [see Fig. 8.2 (ii)].
AC and BD are the two diagonals of the quadrilateral ABCD.
In this chapter, we will study more about different types of quadrilaterals, their
properties and especially those of parallelograms.
You may wonder why should we study about quadrilaterals (or parallelograms)
Look around you and you will find so many objects which are of the shape of a
quadrilateral - the floor, walls, ceiling, windows of your classroom, the blackboard,
each face of the duster, each page of your book, the top of your study table etc. Some
of these are given below (see Fig. 8.3).
Fig. 8.3
Although most of the objects we see around are of the shape of special quadrilateral
called rectangle, we shall study more about quadrilaterals and especially parallelograms
because a rectangle is also a parallelogram and all properties of a parallelogram are
true for a rectangle as well.
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