Question

Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite sides.

Answer 1

Hint: Get the idea about basic definitions and properties of a quadrilateral and its adjacent side, opposite sides, adjacent angles, opposite angles, etc. Using this information to draw a rough diagram of the quadrilateral whose name will be marked as KLMN. Observe the sides which do not have a common vertex to determine the two pairs of opposite sides.

Complete step-by-step solution
Here, we have been asked to draw a rough sketch of a quadrilateral KLMN and we have to mention two pairs of opposite sides. But first, let us know what a quadrilateral is.
In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices. Other games for a quadrilateral are: - quadrangle, tetragon, and 4 – gon. For example: -
 

In the above figure, a quadrilateral named ABCD is drawn.
The sum of all the internal angles of a quadrilateral is \[{{360}^{\circ }}\].
Now, let us know about adjacent sides, opposite sides of a quadrilateral.
(i) Adjacent sides: -
When any two sides of a quadrilateral meet a particular vertex or point then they are called pairs of adjacent sides. In the quadrilateral ABCD, AB and BC can be called a pair of adjacent sides because they meet at a common point B.
(ii) Opposite sides: -
Pair of opposite sides of a quadrilateral are the two sides, which do not meet at a particular point. In the quadrilateral ABCD, AB and CD can be called as a pair of opposite sides.
Now, let us come to the question. We have to draw a rough sketch of a quadrilateral KLMN. So, we can draw it as: -

Note that the two pairs of opposite sides can be: -
1. KL and MN
2. LM and NK

Note: One may note that it is not necessary to start the naming from the bottom, we can start it from any vertex. But remember that we have to be continuous in the alphabets while naming. To draw the diagram we must remember some basic properties of quadrilaterals like the number of sides we require to draw a quadrilateral. Remember the definitions of the opposite and adjacent sides.