 Hello and welcome to the session. In this session we will discuss constructing a quadrilateral. We shall now learn how to construct a quadrilateral when the lengths of four sides, a diagonal of the quadrilateral are given. Let us try to construct a quadrilateral ABCD in which we have AB equal to 4.5 cm, BC equal to 5.5 cm, CD equal to 4 cm, AD equal to 6 cm, and AC equal to 7 cm. First let's draw the rough sketch of the quadrilateral ABCD with the given measurements so that we visualize the quadrilateral. This is the quadrilateral ABCD in which AD is 4.5 cm, BC is 5.5 cm, CD is 4 cm, AD is 6 cm, and the diagonal that is given to us is AC which is of length 7 cm. Now let's start constructing this quadrilateral ABCD. Let's do this step by step. In the first step we draw the triangle ACD using SSS construction condition. So let's now construct the triangle ACD for this. What we do is first we draw AC of length 7 cm. This is the line segment AC which is of length 7 cm. It is the given diagonal of the quadrilateral ABCD. Now as you can see in the rough sketch, AD is of length 6 cm. So from point A we will draw an arc of length 6 cm. Similarly from the point C we will draw an arc of length 4 cm so that we get the point D by the intersection of the two arcs. Let this point of intersection of the two arcs be the point D. Now we join AD and DC so as to get the triangle ACD. Hence we have got the triangle ADC or ACD in which we have AC is of length 7 cm, AD is of length 6 cm, and DC is of length 4 cm. Now in the next step we need to locate the point B. This point B would be on the opposite side to the point D with reference to AC. And for this we have two measurements that is this point B is 4.5 cm away from the point A. So with AC as the centre and radius 4.5 cm we draw an arc. This is the arc drawn with AC as the centre and radius 4.5 cm. Now as you can see in the figure the point B is 5.5 cm away from the point C. So with AC as the centre and radius 5.5 cm we draw an arc. This arc is drawn with AC as the centre and radius 5.5 cm. So point B would lie on both these arcs drawn. We mark this point of intersection of the two arcs as B. Now in the next step we join AB and BC. So as you can see we have joined AB and BC where AB is of length 4.5 cm and BC is of length 5.5 cm. Hence this ABCD is the required quadrilateral. This completes the session. Hope you have understood how we construct a quadrilateral when we lens saw four sides of the quadrilateral are given and one of the diagnosis given to us.