 Hello and welcome to the session. In this session we will discuss some special parallelograms. First special parallelogram that we will discuss is a rhombus. Rhombus is basically a special case of a kite. Now the kite is not a parallelogram as you know. We have that a rhombus is a parallelogram with sides of equal length. This figure ABCD is a rhombus in which we have all the sides are equal. Now since we know that rhombus is a parallelogram so it satisfies all the properties of a parallelogram and also that of a kite, that opposite angles of a rhombus are equal. Now we know that in a parallelogram the diagonals bisect each other. Rhombus also we have that the diagonals of a rhombus are perpendicular bisectors of one another. Let's summarize all the properties of the rhombus using this rhombus ABCD. We have all the sides are equal. AB is equal to BC is equal to CD is equal to DA. And the opposite angles are equal that is angle A is equal to angle C and angle B is equal to angle D. Then we have the diagonals of rhombus are perpendicular bisectors of each other that is we have that AO is equal to OC. Then BO is equal to OD and also angle AOD is equal to angle COD and that is equal to 90 degrees. Then angle AOV is equal to angle BOC and this is equal to 90 degrees. Now next parallelogram that we discussed is a rectangle. Basically a rectangle is a parallelogram with equal angles. Or we can also say that a rectangle is a parallelogram in which every angle is a right angle. Now we know that rectangle is a parallelogram so it satisfies all the properties of the parallelogram. Like we have the opposite sides of the rectangle are of equal length. Now we know that in a parallelogram opposite angles are equal and as we have defined that a rectangle is a parallelogram in which every angle is a right angle. So all the angles of the rectangle are equal and that too of measure 90 degrees. Then we have the diagonals of rectangle bisect each other and also diagonals of a rectangle equal length. Now let's summarize the properties of the rectangle. This ABCD is a rectangle and we have that opposite sides are of equal length that is we have AB is equal to CD and AD is equal to BC. Then all the angles are right angles that is angle A is equal to angle B is equal to angle C is equal to angle D and that is equal to 90 degrees. And the diagonals are of equal length that is we have AC is equal to BD and they bisect each other that is AO is equal to OC and BO is equal to OD. Next parallelogram that we discuss is a square. Basically we say that a square is a rectangle with equal size. So we can also say that square is a parallelogram itself since rectangle is a parallelogram and so it satisfies all the properties of a rectangle and in addition we have that all the sides are of equal length. We say that all the angles of a square are right angles since it is a rectangle. Then we also have that the diagonals of the square are of equal length and also the diagonals of a square are the perpendicular bisectors of each other. Consider the square ABCD now we have all the sides of the square are equal that is AB is equal to BC is equal to CD is equal to DA. All the angles are right angles that is angle A equal to angle B equal to angle C equal to angle D equal to 90 degrees. Then we have diagonals are of equal length that is AC is equal to BD and the diagonals are the perpendicular bisectors of each other that is AO is equal to OC, BO is equal to OD, angle AOD is equal to angle COD is equal to 90 degrees then angle BOC is equal to angle AOB equal to 90 degrees. So these are the three special parallelograms that we have discussed. This completes this session hope you have understood this concept.