 Hello and welcome to the session. Today I will help you with this question. The question says given here are some figures, classify each of them on the basis of the following. Simple curve, simple closed curve, polygon, convex polygon and concave polygon. Now let's see the solution. Now we will consider each figure one by one. First let's see the figure one. We know that simple curve is a curve that does not cross itself. Now as you can see in the figure one no line is crossing itself therefore this figure can be considered as a simple curve. So we have one is a simple curve. Now simple closed curve is the one in which its ends are joined. Now since in figure one all the ends are joined so this can be regarded as a simple closed curve. Now polygon is a closed curve that is made up of only line segments. Now if we look at figure one we can see that there are five line segments in this figure. That means it is made up of only line segments therefore this can be regarded as a polygon. Now a convex polygon is the one in which there are no portions of the diagonals in their exterior. Now in the figure one as we can see that if we join these two points then we get a diagonal in the exterior of this polygon therefore this is not a convex polygon. Whereas a concave polygon is the one in which some of their diagonals lie in the exterior. Now as in the figure one I told you that this point and this point is joined. They have their diagonal in the exterior of their polygon therefore this can be regarded as a concave polygon. Now same is the case with figure two. If we look at the figure two we can see that no line is crossing itself. Hence this figure two can be regarded as a simple curve. Now it's a closed curve also because all its ends are joined therefore it is a simple closed curve. Now it's a polygon because it's made up of four line segments. Now since no diagonals lie in the exterior of this polygon therefore this figure two is the convex polygon and hence it's not a concave polygon. Now let's consider the third figure. In this figure as you can see one curve is inside the other curve therefore this is not a simple curve. Now its ends are also not joined hence this cannot be regarded as a simple closed curve. Now there are no line segments in this curve therefore it's not a polygon either. Now it's not a polygon therefore it's not a convex neither a concave polygon. Now let's see the fourth figure. Now in this figure all the lines are crossing each other therefore this is not a simple curve and hence it's not a simple closed curve. Now it is a polygon because it is made up of line segments therefore this can be regarded as a polygon. Now if we join these points we get their diagonals in the exterior therefore this can be regarded as a concave polygon. Now next we observe the figure five. Now in this figure as we can see that no lines are crossing itself therefore this can be regarded as a simple curve. Now this figure is also a simple closed curve since all its ends are joined. Now this is not a polygon hence it's not a concave or convex polygon because there is no line segment in this figure. Now let's observe the figure six. In figure six as you can see that no line is crossing itself it's a simple curve and since all its ends are joined therefore this is regarded as a simple closed curve and since there are no line segments in this figure therefore this is not a polygon hence it's not a concave or convex polygon. Now looking at figure seven we can see that it is a simple curve because no line is crossing itself and since all its ends are joined therefore this can be regarded as a simple closed curve. Now it's not just made up of only line segments there is a curve also in this figure therefore this cannot be regarded as a polygon and hence it's neither a convex polygon nor a concave polygon. Now lastly we observe the figure eight. In this figure the one line is crossing the other two small curves out there and therefore this cannot be regarded as a simple curve and hence it's not a simple closed curve. Now this is not a polygon because it's just not made up of only the line segments we have two small curves on the outside also and therefore this is not a polygon and hence it's neither a convex nor a concave polygon. Hence the final answer in this case is for a simple curve we have figure one two five six and seven for simple closed curve we have one two five six and seven for polygon we have one two four for convex polygon two for concave polygon it's one and four. Hope you enjoyed the session have a good day.