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I students, welcome to this section where we deal with polygons and quadrilaterals, all right, now

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let's get started with polygons.

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What is a polygon?

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A polygon is a simple closed group made up of only line segments.

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What do we mean with simple?

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It means that it does not cross itself.

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For example, over here, you can see that in this shape, it's crossing itself right now, in this

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shape, it's not crossing itself.

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So this is not a politician and this is a polygon already.

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And it has to be a closed group.

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That is, it cannot be left open.

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For example, this is open.

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So therefore, this is not a polygon.

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All right.

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Now, let's take a few examples to see whether they are polygons or not.

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Is this a polygon?

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Yes, it's simple and closed.

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Right.

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What about this one over here?

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Yes, it's simple and closed all here.

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This is not a polygon because it is not simple, because it is crossing itself and this is not a polygon

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because it's open.

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All right.

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So we have seen that polygons are simple closed curves made up of only nine segments.

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So if you had a shape like this with one part, like a semicircle, then it would not be a polygon because

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a polygon is made up of only nine segments.

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All right.

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Let's move on to classification of polygons.

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Polygons are classified on the basis of number of sites or vertices.

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Now, we are familiar with this.

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If you have three sites, it's called a triangle.

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If you have four sites, it's called a quadrilateral.

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If you have five sites, it's a Pentagon, six sites.

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It's called a hexagon.

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Seven sided polygon is called a have taken an eight sided polygon is called an octagon.

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And nine sided polygon is in Oregon.

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A ten sided polygon is it again.

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And it goes on like that in general.

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We can say that.

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And inside it, Polygon is called and Ingunn.

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All right.

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Now, we will see these storms quite often in many questions.

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Let's move on to quadrilaterals, which are four sided polygons.

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All right.

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So quadrilaterals are four sided polygons.

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Let's take an example over here, OK?

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We have a quadrilateral over here.

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Now, this region is the interior of the quadrilateral.

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This is the exterior of the quadrilateral.

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All right.

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Now let's move on to naming this quadrilateral.

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Let me name the vertices as ABCDE.

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Now, I can call this as quadrilateral A, B, C, D, you can know that the bodices are taken in a

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cyclic manner.

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So, for example, if the quadrilateral was named like this, A, C, B, and then this would be quadrilateral

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AC C.

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Now note that in this case it would be wrong to call this as quadrilateral AC B because the sides have

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to be taken in a cyclic manner.

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You can either call it as A, B, C, D or a DCB and you can start from any vertex, for example.

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You could also call it B, C, D.

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All right, let's move on.

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You can see that a quadrilateral has four sides, four angles, right.

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And forward issus.

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So one of the four sites over here, it's A, B, B, C, C and D, what are the four angles you have?

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Angley angle, B angle see an angle D All right.

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So we have got a fair basic understanding of what a polygon is, what are the classifications of polygons

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and what is the very basics of foresighted polygon called quadrilateral?

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Now let's see, what do we mean with diagonals of a polygon?

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Diagonals are line segments connecting to nonconsecutive.

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What pieces of a polygon?

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Let's take an example.

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Over here you have a rectangle.

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Now this vertex and this vertex are next to each other.

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They are adjacent or they are consecutive.

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So if you join these two together, you do not get a diagonal.

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But this vertex and this vertex is not adjacent to each other.

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So they are nonconsecutive odysseys.

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So if you join these two together or this vertex and this vertex together, you get diagonals.

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So in this foresighted polygon, we get two diagonals.

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All right, let's take another polygon.

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This is a one, two, three, four, five, five sided polygon.

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And we know if I decided polygons call the Pentagon, let's draw all the possible diagonals in the Pentagon.

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That would be this.

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Right.

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We have joined this vertex with this one.

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This one.

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Right.

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We cannot do that with this because that would be a side that is not a diagonal because these two artists

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are adjacent to each other.

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Similarly, this vertex is joined with this one and this one.

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And in that way, you get.

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Diagonals over here.

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Now, what about this polygon over here?

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You have one diagonal over here and you have another diagonal over here, so you have to diagonals.

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Now remember, we are discussed in permutation and combination S. how to find the number of diagonals

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of an incited polygon.

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The formula is NC to minus in.

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Right, because you have invert exists in what it says and to draw a straight line you just need two

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points to selecting.

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Two points out of endpoints is in two and an end sided polygon will have Insight's right.

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So you need to subtract the sides because the sides are not diagonals.

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And that's why the number of diagonals is given by the formula NC to minus.

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And you can see permutation and combination S..

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For more details in this regard.

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All right.

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So we have seen what the polygons we have seen different types of polygons.

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We have seen very few basic things, about a quarter lateral, and we have seen what we mean with diagonals

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and how to find the number of diagonals.

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Now let's see what we mean with regular and irregular polygons.

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A regular polygon is one in which all the sides are equal and all the angles are equal to all the sides

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have to be equal and all the angles have to be equal.

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Now, all the sides being equal, we call that property being equilateral and all the angles being equal.

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We call that property equally angular.

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So a regular polygon is equilateral as well as Igwe angular.

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Now let's take the example of a square and a rectangle.

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Over here we have a square and we know that all the sides of the square are equal and all the angles

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are equal to 90 degrees.

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Therefore, this shape that is the shape of a square is a regular polygon.

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What about a rectangle in a rectangle?

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We know that opposite sides are equal, but all the sides are not equal, right?

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These two sides are equal and these two sides are equal.

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But for it to be regular, all the sides should have equal.

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So a rectangle is not regular or it's an irregular polygon.

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We know that all the angles in a rectangular equal to 90 degrees.

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So it is equally angular, but it is not equilateral and hence the rectangle is an irregular polygon.

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So we have seen the very basics of polygons and quadrilaterals.

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And now let's move on to more interesting properties.