Exploring Symmetry and Patterns

Good morning class. My name is Poonam Divyadi and I am your mathematics teacher. So today we are going to start a new chapter that is chapter 12 and the name of the chapter is Symmetry and Patterns. So let us first discuss what all are the topics we are going to study in this chapter. So first one is Symmetry and Line of Symmetry. Then we will study Symmetry in Plane Shape, Symmetry in Alphabet, Reflection Symmetry, Rotational Symmetry. What is next? what is tessellation and what are patterns. So let's see our first topic that is symmetry. So firstly we will understand the meaning of symmetry. So the definition says a figure is symmetrical if it can be divided into two equal half of the same shape and size. So what do you mean by symmetry? Symmetry means if we divide a figure into equal half then it is known as a symmetry. and the figure which is divided by a line is known as the line of symmetry. So first we will understand the definition of line of symmetry. The line that divides the figure into two parts is called the line of symmetry. As we can see this figure of a tree, so in this figure we can see a line is being drawn and this line divides the figure into two equal parts. If we fold the figure then we can see that the figure exactly matches the other side and it overlaps with each other. So, this line of symmetry. So, this line is known as the line of symmetry. And in this case also, the line drawn is known as the line of symmetry. And if we fold the figure, we will get the same. We will get the same figure and the figure will overlap each other. So, with this, we can say that symmetry is... means a figure, line of symmetry which divides the figure into 2 equal half that is known as symmetry. So, now we will move on to the next topic. Okay, now we are going to see our next topic that is symmetry in plane shape. So, first we will see symmetry in square. So, this is a, so this is a square shape. Okay, so in this square we have 4 line of symmetry. First we will see the horizontal. So we will fold the square in this shape horizontal. Okay. So the square is overlapping each other. Okay. So we can see there is an horizontal line of symmetry in square. So we can see a horizontal line of symmetry in square. The same way if you will fold the square vertically then you will here symmetry in square. So this is a vertical. So if we hold the square in vertical form, the square is overlapping. Okay. So it is symmetrical in shape. So vertical line. Okay. The square has a vertical line of symmetry and square also have planting, two planting line of symmetry. So planting line means planting line means if you will fold the square in this way this is an slanting line okay so from both the sides so this is one of the slanting lines and this is another slanting line if you will fold the square okay so this is another slanting line okay so how we can draw two slanting lines so this is one of the slanting lines As I have shown in this, through this piece of paper. So, this is one of the slanting lines. This is another slanting line. Okay. So, and this was the horizontal line. Okay. And this was the vertical line and this is the horizontal line. So, we have four lines of symmetry in square. Now, we will see the next topic that is rectangle. So this piece of paper is in the form of a rectangle. As you can see, this is in the form of a rectangle. So if we want to draw a horizontal line, so horizontal line means this line. Okay. So if you want to fold this paper in horizontal line, so it would be like this. Okay. So if you fold the rectangle in horizontal line, it would be symmetrical in shape. So, how will garden horizontal line we will draw the horizontal line of rectangle like this. So if we will draw horizontal line the shape would be symmetrical. So if you want to draw a vertical line okay so this was our horizontal line and what would be the vertical line? Vertical line would be like this. If you will fold the rectangle so you will get the vertical line like this. So how we can draw? We can draw the vertical line like this. So we can say that rectangle has two lines of symmetry. Now we'll see the triangle. So triangle can be classified into three forms that is or three types. That is equilateral. Equilateral means which have all the three sides equal and the second one is isosceles triangle. Isosceles triangle means which have two equal sides and the third one was scale and triangle. square and triangle which have no equal size. Okay. So first we'll see equilateral triangle. This is an equilateral triangle and if we will fold it vertically, okay. So if we'll fold it vertically, we'll get the same shape and size. Okay. So the triangle will overlap each other. So this is our one line of symmetry that is vertical line of symmetry. The same way we'll have planting line of symmetry. So if you will fold, if you will fold the equilateral triangle holding the one corner with the other then you will get the planting. So this, this line would be known as a planting, okay. So you will get the planting line that is, if you will fold this corner with this corner you will get a planting line, okay. That is second line of symmetry. The same way if you will hold this corner of triangle and you will match with this corner of triangle you will get a another slanting line of symmetry and this would be so the diagram looks like this okay. So you can try this out at your home also okay. So this was the diagram for equilateral triangle. The same way we have only one line of symmetry in isosceles triangle. So isosceles triangle have only two equal sides so we'll have only vertical line of symmetry in this and calen triangle have no line of symmetry in it okay. So next we'll see the circle. So circles have many lines of symmetry. We can see this diagram with the piece of with the help of this paper. So it is in a form of circle. Okay. So it will fold the circle in a vertical way. Okay. So this is the vertical. We are folding the circle in a vertical line of vertical form. So it could be like this. So this vertical line is equally dividing the figure into two equal half. Okay. The same way it will divide the figure horizontally. So, so this also the figure is overlapping with each other. So we can say that square can be divided horizontally also, vertically also and it can be divided this way also. It can be divided with many number of lines as much as you can draw. Okay. So this also we can draw the lines. So many lines can be drawn as you have seen the Ashoka Chakra of our flag. Okay. So there are so many lines. There are 24 cogs in Ashoka Chakra. So that is also an example of circle. So circle has many lines of symmetry. Okay. So this was about the third topic. Now we will see our next topic. Now we will see our next topic that is symmetry in alphabet. So first one is horizontal line. So now we'll see the symmetry in alphabet. So first one is horizontal line. So first letter is B. So if we divide B horizontally then only it will be symmetrical in shape and if we divide or draw horizontal line then only if we fold C horizontally then only we'll get the symmetrical in shape. the same way we will draw horizontal we can divide letter D in symmetry by drawing horizontal line. The same way E and the same way K. Okay. Now the second one is vertical line. As we have drawn, as we have seen horizontal line in alphabet, now we will see vertical line in alphabet. So if you will draw, if you will see letter A, if you will draw a vertical line and then if we will fold letter A then it will overlap and if we will draw horizontal line then it will not overlap each other. So only vertical line can be drawn in alphabet A. The same way letter M and the same way letter T will have vertical line and the same way letter U will have vertical line. So, now we will see two line of symmetry. So, in two line of symmetry we can fold the letter in by two ways that is vertically. If you want to fold letter H vertically so, it will be overlapping. So, it will form a vertical line and if you want to fold letter H horizontally then also it will be overlapping each other. So, this is the case of two lines of symmetry. The same way letter I is also a case of two line of symmetry that is vertically if we fold and if we fold horizontally then it will be overlock overlapping each other. The same way if we will see if we draw a line vertically of letter X letter O then It will be overlapping each other in the same way if we will draw a horizontal line and if we fold horizontally letter X, it will be overlapping. The same way letter X vertically and horizontally. It will be overlapping each other. So now we will see the last one that is no line of symmetry. So there will be no line of symmetry in these letters. Okay. Like if we will draw. If you want to draw vertically, okay, if you want to draw the letter vertically, then it will not overlap together. If you want to fold the letter F, so you won't be able to fold it, it would not overlap. The same with letter G, letter J and letter L. These letters will have no line of symmetry, okay. So now we will see our next topic. Now we will see our next topic that is reflection symmetry. An image looks the same on either side of a line. It is easy to see because one half is the reflection of the other half. So this means that if we are drawing an image or if we have been given an image which is half and we have been given a line of symmetry. So we can draw the other half by seeing the symmetry. Given figure by seeing the given half side of the figure we can draw other side of the figure also. That is we have been given a diagram the half side. Okay. So we have been given the line of symmetry so we can draw the other part by seeing the given part. The same way we have been given the line of symmetry and half letter T. So we can draw. the another half by seeing the given half. So this is known as a reflection symmetry. Now we will see the next topic that is rotational symmetry. The number of times an object looks the same while rotated in one round is called order of rotational symmetry. So this definition says if an object is rotated in one round it comes to the actual position that is known as the rotational symmetry. Like for example, this is an duster. Okay. So if we are rotating this duster in this way, so this is up to 90 degrees. So now again we are going to rotate, then it comes to 180 degrees. And again we are going to rotate it, then it comes to 270. And then again, if we are rotating, it comes back to the actual position, that is to the position which was it was in the earlier. So here is an example. So this is a narrow and if we are going if we are rotating it to 90 degrees. then it becomes like this and then if you are rotating it 180 degree, it becomes, the arrow goes down and if you are rotating it 270 degrees, the arrow becomes, goes this side and if you are rotating again, then it comes to 360 degree that it comes to its actual position. So, this is known as the rotational symmetry. Now, we will see the next. What do you mean by next? First, let us see the definition. That is a net is a two dimensional shape that can be folded to form a three dimensional shape or solid. So we can take the example as this is a cube and this is the net form of the cube. So here we can take the example as cube has six faces and eight vertex and twelve edges. So a net can... So a net is a two dimensional shape that can be folded into two that can be folded and form a three dimensional shape. So we can take the example as this is a form of net. Okay. So if you want to fold and through this net we can so from this net we can make a cube. So it has six faces. So we can see that it has six faces as one, two. 3, 4, 5 and 6. So if you want to create a cube from this net, so what we can do is we can fold this like this and this one will go, it will go upward and this will become a cube. Okay. So how does it become a cube? This becomes a cube from all the sides. Okay. So this was about next. Now we'll see our next topic. Now we'll see our next topic that is tessellation. The design that fit into each other without any gaps or overlapping are called tessellation. Okay. So the design that fits each other without any gap is known as tessellation. So this figure is of tessellation because it is not having any gap and this is not the figure of tessellation. as it is having gas in between. Okay. So this was about tessellation. Now we will see our last topic that is pattern. A pattern is a sequence of repeated numbers or shapes or objects. Patterns can be seen everywhere around us. So pattern is a form that follows some pattern. Okay. Some shapes or some numbers. That is, for example. 2, then it comes 4, then it comes 6, then it came 8. So what would be the next 4 numbers? In this we can see that a pattern is being followed that is difference between these two numbers is 2. That is if we will add 2 plus 2, we will get 4. The same way if we will add 4 plus 2, we will get 6. The same way if we will add 6 plus 2, we will get 8 and the same way if we will add 8 plus 2 we will get 10 and the same way if we will add 10 plus 2 we will get 12 and the same way if we will add 12 plus 2 we will get 14 and if we will add 14 plus 2 we will get 16. So in this pattern we have seen that there is a gapping or the pattern gapping of two in each case. We have seen that a pattern is being followed in this example. So this was it for chapter 12 that is symmetry and patterns. So we end our power chapter here. So thank you all for watching.

Good morning class. My name is Poonam Divyadi and I am your mathematics teacher. So today we are going to start a new chapter that is chapter 12 and the name of the chapter is Symmetry and Patterns.

So let us first discuss what all are the topics we are going to study in this chapter. So first one is Symmetry and Line of Symmetry. Then we will study Symmetry in Plane Shape, Symmetry in Alphabet, Reflection Symmetry, Rotational Symmetry.

What is next? what is tessellation and what are patterns. So let's see our first topic that is symmetry.

So firstly we will understand the meaning of symmetry. So the definition says a figure is symmetrical if it can be divided into two equal half of the same shape and size. So what do you mean by symmetry? Symmetry means if we divide a figure into equal half then it is known as a symmetry.

and the figure which is divided by a line is known as the line of symmetry. So first we will understand the definition of line of symmetry. The line that divides the figure into two parts is called the line of symmetry. As we can see this figure of a tree, so in this figure we can see a line is being drawn and this line divides the figure into two equal parts. If we fold the figure then we can see that the figure exactly matches the other side and it overlaps with each other.

So, this line of symmetry. So, this line is known as the line of symmetry. And in this case also, the line drawn is known as the line of symmetry.

And if we fold the figure, we will get the same. We will get the same figure and the figure will overlap each other. So, with this, we can say that symmetry is...

means a figure, line of symmetry which divides the figure into 2 equal half that is known as symmetry. So, now we will move on to the next topic. Okay, now we are going to see our next topic that is symmetry in plane shape.

So, first we will see symmetry in square. So, this is a, so this is a square shape. Okay, so in this square we have 4 line of symmetry.

First we will see the horizontal. So we will fold the square in this shape horizontal. Okay.

So the square is overlapping each other. Okay. So we can see there is an horizontal line of symmetry in square.

So we can see a horizontal line of symmetry in square. The same way if you will fold the square vertically then you will here symmetry in square. So this is a vertical.

So if we hold the square in vertical form, the square is overlapping. Okay. So it is symmetrical in shape. So vertical line. Okay.

The square has a vertical line of symmetry and square also have planting, two planting line of symmetry. So planting line means planting line means if you will fold the square in this way this is an slanting line okay so from both the sides so this is one of the slanting lines and this is another slanting line if you will fold the square okay so this is another slanting line okay so how we can draw two slanting lines so this is one of the slanting lines As I have shown in this, through this piece of paper. So, this is one of the slanting lines.

This is another slanting line. Okay. So, and this was the horizontal line. Okay. And this was the vertical line and this is the horizontal line.

So, we have four lines of symmetry in square. Now, we will see the next topic that is rectangle. So this piece of paper is in the form of a rectangle.

As you can see, this is in the form of a rectangle. So if we want to draw a horizontal line, so horizontal line means this line. Okay.

So if you want to fold this paper in horizontal line, so it would be like this. Okay. So if you fold the rectangle in horizontal line, it would be symmetrical in shape.

So, how will garden horizontal line we will draw the horizontal line of rectangle like this. So if we will draw horizontal line the shape would be symmetrical. So if you want to draw a vertical line okay so this was our horizontal line and what would be the vertical line?

Vertical line would be like this. If you will fold the rectangle so you will get the vertical line like this. So how we can draw?

We can draw the vertical line like this. So we can say that rectangle has two lines of symmetry. Now we'll see the triangle. So triangle can be classified into three forms that is or three types. That is equilateral.

Equilateral means which have all the three sides equal and the second one is isosceles triangle. Isosceles triangle means which have two equal sides and the third one was scale and triangle. square and triangle which have no equal size.

Okay. So first we'll see equilateral triangle. This is an equilateral triangle and if we will fold it vertically, okay. So if we'll fold it vertically, we'll get the same shape and size.

Okay. So the triangle will overlap each other. So this is our one line of symmetry that is vertical line of symmetry.

The same way we'll have planting line of symmetry. So if you will fold, if you will fold the equilateral triangle holding the one corner with the other then you will get the planting. So this, this line would be known as a planting, okay.

So you will get the planting line that is, if you will fold this corner with this corner you will get a planting line, okay. That is second line of symmetry. The same way if you will hold this corner of triangle and you will match with this corner of triangle you will get a another slanting line of symmetry and this would be so the diagram looks like this okay. So you can try this out at your home also okay.

So this was the diagram for equilateral triangle. The same way we have only one line of symmetry in isosceles triangle. So isosceles triangle have only two equal sides so we'll have only vertical line of symmetry in this and calen triangle have no line of symmetry in it okay.

So next we'll see the circle. So circles have many lines of symmetry. We can see this diagram with the piece of with the help of this paper.

So it is in a form of circle. Okay. So it will fold the circle in a vertical way. Okay.

So this is the vertical. We are folding the circle in a vertical line of vertical form. So it could be like this. So this vertical line is equally dividing the figure into two equal half. Okay.

The same way it will divide the figure horizontally. So, so this also the figure is overlapping with each other. So we can say that square can be divided horizontally also, vertically also and it can be divided this way also. It can be divided with many number of lines as much as you can draw.

Okay. So this also we can draw the lines. So many lines can be drawn as you have seen the Ashoka Chakra of our flag. Okay.

So there are so many lines. There are 24 cogs in Ashoka Chakra. So that is also an example of circle.

So circle has many lines of symmetry. Okay. So this was about the third topic. Now we will see our next topic.

Now we will see our next topic that is symmetry in alphabet. So first one is horizontal line. So now we'll see the symmetry in alphabet. So first one is horizontal line.

So first letter is B. So if we divide B horizontally then only it will be symmetrical in shape and if we divide or draw horizontal line then only if we fold C horizontally then only we'll get the symmetrical in shape. the same way we will draw horizontal we can divide letter D in symmetry by drawing horizontal line.

The same way E and the same way K. Okay. Now the second one is vertical line. As we have drawn, as we have seen horizontal line in alphabet, now we will see vertical line in alphabet.

So if you will draw, if you will see letter A, if you will draw a vertical line and then if we will fold letter A then it will overlap and if we will draw horizontal line then it will not overlap each other. So only vertical line can be drawn in alphabet A. The same way letter M and the same way letter T will have vertical line and the same way letter U will have vertical line. So, now we will see two line of symmetry. So, in two line of symmetry we can fold the letter in by two ways that is vertically.

If you want to fold letter H vertically so, it will be overlapping. So, it will form a vertical line and if you want to fold letter H horizontally then also it will be overlapping each other. So, this is the case of two lines of symmetry. The same way letter I is also a case of two line of symmetry that is vertically if we fold and if we fold horizontally then it will be overlock overlapping each other. The same way if we will see if we draw a line vertically of letter X letter O then It will be overlapping each other in the same way if we will draw a horizontal line and if we fold horizontally letter X, it will be overlapping.

The same way letter X vertically and horizontally. It will be overlapping each other. So now we will see the last one that is no line of symmetry.

So there will be no line of symmetry in these letters. Okay. Like if we will draw.

If you want to draw vertically, okay, if you want to draw the letter vertically, then it will not overlap together. If you want to fold the letter F, so you won't be able to fold it, it would not overlap. The same with letter G, letter J and letter L.

These letters will have no line of symmetry, okay. So now we will see our next topic. Now we will see our next topic that is reflection symmetry.

An image looks the same on either side of a line. It is easy to see because one half is the reflection of the other half. So this means that if we are drawing an image or if we have been given an image which is half and we have been given a line of symmetry. So we can draw the other half by seeing the symmetry.

Given figure by seeing the given half side of the figure we can draw other side of the figure also. That is we have been given a diagram the half side. Okay. So we have been given the line of symmetry so we can draw the other part by seeing the given part.

The same way we have been given the line of symmetry and half letter T. So we can draw. the another half by seeing the given half.

So this is known as a reflection symmetry. Now we will see the next topic that is rotational symmetry. The number of times an object looks the same while rotated in one round is called order of rotational symmetry. So this definition says if an object is rotated in one round it comes to the actual position that is known as the rotational symmetry.

Like for example, this is an duster. Okay. So if we are rotating this duster in this way, so this is up to 90 degrees.

So now again we are going to rotate, then it comes to 180 degrees. And again we are going to rotate it, then it comes to 270. And then again, if we are rotating, it comes back to the actual position, that is to the position which was it was in the earlier. So here is an example. So this is a narrow and if we are going if we are rotating it to 90 degrees.

then it becomes like this and then if you are rotating it 180 degree, it becomes, the arrow goes down and if you are rotating it 270 degrees, the arrow becomes, goes this side and if you are rotating again, then it comes to 360 degree that it comes to its actual position. So, this is known as the rotational symmetry. Now, we will see the next. What do you mean by next?

First, let us see the definition. That is a net is a two dimensional shape that can be folded to form a three dimensional shape or solid. So we can take the example as this is a cube and this is the net form of the cube. So here we can take the example as cube has six faces and eight vertex and twelve edges.

So a net can... So a net is a two dimensional shape that can be folded into two that can be folded and form a three dimensional shape. So we can take the example as this is a form of net.

Okay. So if you want to fold and through this net we can so from this net we can make a cube. So it has six faces.

So we can see that it has six faces as one, two. 3, 4, 5 and 6. So if you want to create a cube from this net, so what we can do is we can fold this like this and this one will go, it will go upward and this will become a cube. Okay.

So how does it become a cube? This becomes a cube from all the sides. Okay. So this was about next. Now we'll see our next topic.

Now we'll see our next topic that is tessellation. The design that fit into each other without any gaps or overlapping are called tessellation. Okay.

So the design that fits each other without any gap is known as tessellation. So this figure is of tessellation because it is not having any gap and this is not the figure of tessellation. as it is having gas in between. Okay. So this was about tessellation.

Now we will see our last topic that is pattern. A pattern is a sequence of repeated numbers or shapes or objects. Patterns can be seen everywhere around us. So pattern is a form that follows some pattern.

Okay. Some shapes or some numbers. That is, for example. 2, then it comes 4, then it comes 6, then it came 8. So what would be the next 4 numbers?

In this we can see that a pattern is being followed that is difference between these two numbers is 2. That is if we will add 2 plus 2, we will get 4. The same way if we will add 4 plus 2, we will get 6. The same way if we will add 6 plus 2, we will get 8 and the same way if we will add 8 plus 2 we will get 10 and the same way if we will add 10 plus 2 we will get 12 and the same way if we will add 12 plus 2 we will get 14 and if we will add 14 plus 2 we will get 16. So in this pattern we have seen that there is a gapping or the pattern gapping of two in each case. We have seen that a pattern is being followed in this example. So this was it for chapter 12 that is symmetry and patterns.

So we end our power chapter here. So thank you all for watching.

Transcript for:Exploring Symmetry and Patterns

Transcript for:
Exploring Symmetry and Patterns