Types of Quadrilaterals
Now let’s understand different types of quadrilaterals. We’ll start with a trapezium,
A trapezium is a quadrilateral where one pair of opposite sides are parallel. So if we visualize, it will look like this, this will be a trapezium, where these two sides are parallel and these two sides are non parallel. Now if these two non parallel sides, if they are equal in length then it is called an isosceles trapezium. Now parallelogram is what I’ll discuss next, when both the pairs of opposite sides are parallel then that kind of quadrilateral is called a parallelogram. So if we visualize it will look like this, these two are parallel, these two are parallel, this is parallelogram.
So here these two sides are parallel, these two sides are parallel that means both the pairs are parallel here so this is a parallelogram. It’s very easy to understand. So trapezium is when one pair of opposite sides are parallel, parallelogram is where both the pairs are parallel. Now to make it interesting let me show how we can convert an isosceles trapezium into a parallelogram with same area. And I’m sure you like it. Let’s take an isosceles trapezium like this, these two sides are parallel these two are non parallel. Drop a perpendicular, this point join with the mid-point of this side, shade this triangle, just flip this shaded triangle there you get a parallelogram with the same area, because there is no change here right? So as you already know parallelograms are nothing but where is the both pairs of opposite sides are parallel. Now let’s look at different types of parallelograms. In a parallelogram, so let’s see a parallelogram like this where these two are parallel these two are parallel. Now if I just cut here and if I make all four side equal this is called rhombus. Rhombus is a parallelogram where all four sides are equal. Now rectangle is a parallelogram where one angle is 90. Effectively when one angle is 90 degree, all four angles will be 90 degrees, and equal, so let’s take a parallelogram like this, and if I move it like this it will become 90 here, all four will become 90 this is rectangle. Now to make it interesting let me show you how we can convert a parallelogram into a rectangle, with the same area. So take a parallelogram like this drop a perpendicular, shade this triangle, cut the triangle and just slide it like this you will get a rectangle with the same area, very easy right and interesting—2;45 just make you think better just to make you connect better let me show you how we can convert let me also show you how we can convert an isosceles trapezium into a rectangle with the same area. This also very very interesting. So for that let’s visualize an isosceles trapezium like this, now drop two perpendiculars passing through the mid-points of both the non parallel sides. So you get two triangles here shade the triangles rotate these two triangles like this there you get a perfect rectangle with the same area. Very interesting. Now next we look at squares, what is squares, nothing but in simple language, a parallelogram you convert this into a rhombus and a rectangle together you get a square. So what is rhombus. Rhombus is where all the four sides are equal and rectangle where all the four angles are equal and equal 90 degree. If you take both together you get a square. In a square all four sides will be equal all four angles will be equal and 90 degree, and that kind of parallelogram is a square. Now to simplify let’s visualize this, take a parallelogram, and if I cut here and make all the four equal I’ll get rhombus, just move it here to make it 90, so I get a square. Because now it is all the four sides are equal and all four angles are equal so we get a square like that. Very simple right? How we are converting a parallelogram into a special parallelogram which is called a square. Because square is also finally a parallelogram. Just like all rectangles are parallelograms, all rhombus parallelograms all squares are obviously parallelograms. We also know that when two pairs of adjacent sides are equal like this, that is these two are equal these two are equal then we call it a kite, now this is not like a trapezium because neither like a trapezium nor like a parallelogram, because in a parallelogram both pairs of opposite sides need to be parallel. And in trapezium one pair of opposite sides needs to be parallel. In this case only adjacent sides are equal right? These two are equal in length these two are equal in length so this is called a kite. So now we know all types of quadrilaterals starting from trapezium to kites. Now just to make you understand that using a very simple diagram may be you can represent them like this, if we just summarize all types of quadrilaterals and if I present all them in on screen it will look like this. A trapezium where one pair of opposite sides are parallel, now if we look at different types of parallelograms, parallelograms is where both pairs of opposite sides are parallel over there if all sides are equal we get rhombus if all the angles are equal to 90 degree we get rectangle now if it is brought together we get a square where all four sides are equal and all four angles are equal to 90, and kites are any way neither trapeziums nor parallelograms kites are where adjacent sides are equal and they look like this, using Venn diagram if you want to represent quadrilaterals it will look like this now trapeziums, parallelograms, some of them will be rhombus, some of them will be rectangles, by bring them together the intersection that is when it is rhombus and a rectangle it’s a square and kites are we have to represent as circle outside and they will the Venn diagrams on quadrilaterals will look like this it’s very easy to understand, if you know Venn diagram you can easily connect how they are related.