### Understanding Quadrilaterals

Now, to make it interesting…let me show how to convert an ‘isosceles trapezium’ into a parallelogram with the same area…and I’m sure you’ll 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 the shaded triangle…there you get a parallelogram with the same area…because there is no change here…right? so…very simple and interesting…

So, as you already know, parallelograms are nothing but…where is…both ways of opposite sides are parallel… now let’s look at different types of parallelograms… In a parallelogram…so let’s take 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 sides equal… this is called a rhombus…a rhombus is a parallelogram where all four sides are equal…

Now, a rectangle is a parallelogram where one angel is 90… effectively, when one angel is 90, all four angles will be 90 degrees and equal…so let’s take a parallelogram like this…if I just move it like this…it will become 90 here…all four will become 90… and this is a 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…so you get a rectangle with the same area…very easy…right? …and interesting…intuitive…

Just to 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 of…with the same area…this is 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 we 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…so, what is a square..? nothing but…in simple language, a parallelogram…you convert it into a rhombus and a rectangle together…you get a square…to simplify…let’s visualize this…take a parallelogram…now if I cut here…and if I make all the four equal… I will get a rhombus…just move it here…to make it 90 …. so I get a square…because now, it’s all the four sides are equal and all four angles are equal…so we get a square like that…we also know that…when two pairs of adjacent sides are equal…like this…that’s, these two are equal…and these two are equal…then we call it a kite…now this is not like a trapezium, because….this is neither like a trapezium nor like a parallelogram…because in a parallelogram, both pairs of opposite sides needs to be parallel….and in a 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 the types of quadrilaterals…starting from trapezium to kites…now, just to make you understand that using….a verify simple diagram…may be you can represent them like this…if we just summarize all types of quadrilaterals…and if I present them all in one 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 are…pairs of opposite sides are parallel…now, over there, in parallelogram if four sides are equal, we get rhombus…if all the angles are equal to 90, we get a rectangle…now if its both together, then we get a square where all four sides are equal and all four angles are equal to 90… and kites are anyway neither trapeziums nor parallelograms…kites are where adjacent sides are equal and they look like this…

Using Venn diagrams 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…if I bring them together…the intersection…that is, when it’s a rhombus and a rectangle…it’s a square…and kites are…we’ll have to represent in a separate circle outside…and they ‘ll…the Venn diagrams on quadrilaterals….will look like this…it’s very easy to understand…if you know Venn diagrams…you can easily connect how they are related.