Video transcript- [Voiceover] Which shapes are symmetrical? To answer this, we need to know what it means for a shape to be symmetrical. A shape is symmetrical if it has at least one line of symmetry, a line of symmetry. And now that answer is only helpful if we know what a line of symmetry is. So let's talk about it. A line of symmetry is a line where we can fold the image and have both halves match exactly. Let's look at an example. Let's maybe draw a circle and then we could put a line on that circle. Let's draw a line maybe somewhere like this. This line is a line of symmetry if we can take one side of the line and fold it onto the other and have them match exactly. So let's take one side, doesn't matter which one, let's say the top side, and if we were gonna fold this top side down onto the bottom, would it match exactly what is shown under here? Let's see, it would probably look something like this. And does that match exactly? No, definitely not. So this is not a line of symmetry. Let's try another line. Maybe if we drew a line and we'll try to get as close down the center as we can here like this. Try to be as close to the center as possible and here if we took one side, again it doesn't matter which side, let's say over here, let's say the left side, and we folded this left side onto the right side, would it match exactly and if our line truly was in the center of the circle, then yes it would, which means that this line is a line of symmetry and because we can draw this line of symmetry on our circle, it means that our circle is symmetrical. Shapes are symmetrical if they have at least one line of symmetry and circles have many, many, many lines of symmetry. There was many places we could have drawn a line and folded it so that it worked so the two halves matched exactly. But here's one and as soon as we find one, we know we have a symmetrical shape. So let's go back to the shapes we were given. We can start with the triangle. If we draw a line, maybe a vertical line, let's try to draw it as close to the middle as possible, something like this, and we fold, let's take one side, if we fold this side over, these two lines might match up nicely, but this line here is gonna create something more like this, which does not match what's shown over here, so that's not a line of symmetry, and anywhere else vertical, same thing. We're not gonna have it lined up. So let's try maybe a horizontal line. Is there anywhere horizontally we could draw a line? And again, I think we're gonna see the same thing that the top and the bottom of the line are not gonna match up exactly. So maybe one last thing we could try is a diagonal line, something like this. Maybe this could be our line of symmetry. If we fold this bottom side, this might line up pretty nice here and then this side is gonna do something like this. So it's close, it's the closest we've gotten, but still does not match exactly. For it to be a line of symmetry, it needs to match exactly. So we weren't able to find a way to draw a vertical line or a horizontal line or even the diagonal line. So this shape has no lines of symmetry. So we can say it is not symmetrical. Moving on to the rectangle. Let's try here. Again, this time maybe we'll try a horizontal line. We can draw one right here and if that line truly is in the middle, which is what I've tried for, then this side should match up nicely to this one, across the top should match across the bottom and these sides, if I was right at the halfway point, should fold over each other also. So it has a line of symmetry so it is symmetrical. It has more than one line of symmetry. It has another one in the middle right here. But once we've found one, we know that it's symmetrical. And finally, let's look, we have a pentagon. Here again, trying a line in the middle in some way is usually a good place to start. We can try to draw a line right if this is right down the center here. Then if we folded this side, should line up nicely to this side, this side and this side would overlap and these two would match exactly. So again, has one line of symmetry so it is symmetrical and just like the rectangle, this one had quite a few lines of symmetry. Here's another line of symmetry, here's another line of symmetry, here's one more line of symmetry and so it has quite a few. It has it looks like one, two, three, four lines of symmetry, but as long as it has one, it is symmetrical. So of the shapes we were given, the rectangle and the pentagon were symmetrical. Show
In mathematics, an object is said to have symmetry if it can be divided into two identical halves. The line that divides the object into its identical halves is called the line of symmetry. For example, in the given image, the line passing through the middle of the flower is its line of symmetry. A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts. We also call this line the axis of symmetry or mirror line because it divides the figure symmetrically, and the divided parts look like mirror reflections of each other. More line of symmetry examples are shown in the figure below. A figure or shape that can be divided into two equal parts by a line is called SYMMETRIC figures. The shapes and objects that are irregular and do not resemble each other when divided into two parts are called ASYMMETRIC. The line of symmetry can be categorized based on the basis of its orientation. Horizontal Line of Symmetry: If a horizontal line divides an object into two identical halves, it is called a horizontal line of symmetry. That means the horizontal line of symmetry goes from left to right (or vice versa) in an object. Vertical Line of Symmetry: If a vertical line divides an object
into two identical halves, it is called a vertical line of symmetry. That means that the vertical line goes from top to bottom (or vice versa) in an object and divides it into its mirror halves. Diagonal Line of Symmetry: If a diagonal line divides an object into two identical halves, it is called a diagonal line of symmetry. That means the diagonal line of symmetry goes sideways or slanting in an object. The line of symmetry produces reflections that coincide. A shape or an object can have multiple lines of symmetry as per its structure. Shapes with one line of symmetry have only one line that divides them into identical parts. Shapes with multiple lines of symmetry have more than one line that divides them equally. The axis of symmetry can be horizontal, vertical or diagonal. For example, Axis of symmetry in common two-dimensional
geometrical shapes are given below: Geometric
shapes can have more than one line of symmetry. Let us study some geometric shapes with one and multiple axes of symmetry. Example 1: How many lines of symmetry do the given figure
have? Solution: The given figure only has one line of symmetry.  Example 2: Identify whether the given line of symmetry is a vertical, horizontal, or diagonal line of symmetry. Solution: The given line is a vertical line of symmetry. Example 3: Write three capital letters in the English alphabet have no lines of symmetry? Solution: The three letters in the English alphabet that have no lines of symmetry are P, G, and J. Example 4: Write three capital letters in the English alphabet with horizontal and vertical lines of symmetry. Solution:The English alphabets with horizontal and vertical lines of symmetry are H, I and O. Practice Problems0 1 2 3 Correct answer is: 1 A D R U Correct answer is: R Square Kite Rhombus Parallelogram Correct answer is: Rhombus A B C D Correct answer is: A ConclusionLines of symmetry can help children understand and create patterns. It teaches a sense of balance and order and opens them up to the natural world where symmetry abounds—insects, seashells, and leaves, to name a few. Frequently Asked QuestionsWhat is the maximum number of lines of symmetry in an object? The number of lines of symmetry depends on the shape or figure. For example, an isosceles triangle has one line of symmetry, the rectangle has two lines of symmetry, and the circle has an infinite line of symmetry. Are there shapes that have no lines of symmetry? The shapes or objects that are irregular and do not resemble each other when divided into two parts are called ASYMMETRIC. Such shapes do not have a line of symmetry. A scalene triangle, a parallelogram, and a trapezium are examples of shapes that have no lines of symmetry. How do you find the line of symmetry for a shape? Fold the shape so that one half is identical to the other half. The line along which you have folded can be called a line of symmetry. There can be more than one such line or line of symmetry. How many lines of symmetry does a regular polygon have? In a regular polygon, all sides and angles are equal. If it has “n” number of sides, it will also have “n” number of lines of symmetry. For example, a square with four equal sides has four lines of symmetry, and a regular pentagon has five lines of symmetry. How Can You Identify symmetry in a figure?A shape or an object has symmetry if it can be divided into two identical pieces. In a symmetrical shape, one-half is the mirror image of the other half. The imaginary axis or line along which the figure can be folded to obtain the symmetrical halves is called the line of symmetry.
How do you explain what symmetry is?In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
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How can we tell that a figure is a symmetry
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