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How to find Symmetry (Video & Practice Questions)

TranscriptPractice

Hey there! Welcome to this video on symmetry. Let’s get started!

What happens when I take these two shapes,

and I split them in half?

The shapes are identical in size and shape, right? I can see this more clearly by folding the images on top of each other.

So, we can see that when I have drawn a line, I have created two congruent shapes. Congruent means that the two shapes are identical. When you are able to draw a straight line through the center of a shape, and it creates two congruent shapes, then these two shapes are also symmetrical.

Symmetry comes from the Greek word symmetria meaning “a similar agreement of parts.”

Symmetry, just like congruent shapes, means that one shape becomes exactly like the other when you move it in some way. The movement could be a turn, a flip, or a slide.

When a shape is not symmetrical, then this is referred to as asymmetrical.

Some shapes have lines of symmetry. A line of symmetry is a line that splits the shape in half, creating an identical shape. Some shapes only have one line of symmetry, some have two, and some have several!

However, to draw a line of symmetry, we must first identify the point of symmetry. This is because the point of symmetry marks the point that the lines of symmetry could pass through.

A point of symmetry is when there is a position or central point on an object or shape where the central point splits the object into two identical parts. And, every single line and angle on the other side of the central point is the same exact distance from the central point on each side.

That was a lot. Let’s take a look at what I mean.

Where both identical lines of the cross intersect, we can see that there is a point of symmetry, but let’s take a look at the definition to make sure.

So let me draw this line here, this point of symmetry.

Okay, does the point split the cross into two identical, or congruent, shapes? Well, if we imagined folding it over across this point, it would then split it in half. So, check!

Is every single line or angle of the cross the exact same distance from the point on each side?

So “are all these angles congruent and the same exact distance from this point” is our question.

Based on what we can see, it definitely appears that way. However, to be one hundred percent sure, we would need to measure every single line and angle. But, for this exercise, I have used an example where we are assuming all the lines and angles are the exact same distance, so check!

Now, let’s practice finding lines of symmetry.

Since we’ve already found the point of symmetry on the cross, let’s see how many lines of symmetry it has. How many times can we split the cross, and get identical parts?

That gives us: 1, 2, 3, 4. So there are 4 lines of symmetry here, but after 4, there are no other lines that would give us two identical parts.

Great job!

Let’s try another.

How many lines of symmetry does the dog have? Or how many lines can you draw that create multiple identical parts?

Let’s see. If we did it through the center horizontally, we wouldn’t get two identical parts because he has a lower half and then a head. So if we do it through the center from the top to the bottom, we’ll get two eyes, two parts of the nose, two halves of the mouth, two halves of the body, and two of the legs.

So we can see there’s one line of symmetry.

If there were any more lines, then we would not have identical parts.

What about the side of the dog? Do you see any lines of symmetry?

No. Each end of the dog has different-shaped parts. The head is different than the tail. Let’s move on.

Okay, now what about this thought bubble?

Is there a line you can draw to create two identical parts? No.

Let’s see how many lines we can draw to split this hexagon into identical parts.

1, 2, 3, 4, 5, 6.

You guys have done a really great job.

Keep practicing by looking for shapes that are symmetrical in your classroom, in your house, outside, or wherever you are.

Symmetry is everywhere, and it’s very important. Architects and engineers use symmetry to design sturdy buildings and other objects. Interior designers use symmetry and asymmetrical design to make their work more appealing to look at. People everywhere use symmetry in some way.

I hope that this video was helpful. See you next time!

Question #1:

 
How many lines of symmetry does a square have?

Show Answer

Answer:

A square can be folded in half horizontally, vertically, or over each diagonal shown. Therefore, the square has four lines of symmetry.

Hide Answer

Question #2:

 
Which letter has exactly two lines of symmetry?

Show Answer

Answer:

The letter X has a vertical line of symmetry and a horizontal line of symmetry. When an imaginary line passes through the center of the letter X horizontally and vertically, it creates identical halves. The other answer options have no lines of symmetry.

Hide Answer

Question #3:

 
Which image shows a dotted line that is not a line of symmetry?

Show Answer

Answer:

A line of symmetry splits a shape in half, creating two identical shapes. The two halves of the S shown are not identical. Therefore, the dotted line in Choice D is not a line of symmetry.

Hide Answer

Question #4:

 
Kate is a graphic designer and is creating a logo with the letter H. She needs to identify its lines of symmetry so she can arrange the logo with precision. How many lines of symmetry are in the letter H?

Show Answer

Answer:

The letter H contains two lines of symmetry: a vertical and a horizontal line of symmetry.

Hide Answer

Question #5:

 
Juan is learning about symmetry in his math class. For homework, his teacher tells the class to find examples of objects that have a point of symmetry. The next day in class, Juan says he found four objects with a point of symmetry: the letter A, a King of Hearts playing card, an hourglass, and a plate. His teacher tells him that all his objects have a point of symmetry except for one. Which of Juan’s objects does not have a point of symmetry?

The letter A

A King of Hearts playing card

An hourglass

A circular plate

Show Answer

Answer:

Point symmetry occurs when every part of an image has a matching part that is the same distance from the central point but in the opposite direction. The letter A does not have an origin point that divides the figure to create two matching parts in opposite directions. The rest of the objects listed do have point symmetry.

Hide Answer

 

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Symmetry | 3rd Grade Math

Not all pictures and shapes are symmetrical.

For example, when we fold this triangle along the red line, the two parts are not equal. ❎

We can try drawing another line.

The two parts still do not match. ❎

Let’s draw another line.

The parts still don’t match. ❎

No matter where we try to draw a line, the two parts don’t match. 

This triangle has no line of symmetry, so it’s not symmetrical.

Finding the Line of Symmetry

Can you tell if this picture has symmetry?

Let’s find out by drawing lines on it. 😀

We can draw a vertical line.

Is this a line of symmetry?

It is! Both sides match exactly. ✅

We can draw another line from left to right.

The part above the line matches the part under it. 

So, this horizontal line is also a line of symmetry. ✅

Now, let’s try drawing a diagonal line.

Did you notice something?

Yes! The parts on both sides of the line still match.

This picture has more than one line of symmetry.

It is definitely symmetrical! 👍

      A picture or shape can have more than 1 line of symmetry, but it only needs 1 line of symmetry to be symmetrical.

Now, how many lines of symmetry does this shape have?

We see that the vertical line is a line of symmetry. ✅

Do you think there are more?

We can try to draw a horizontal line.

It’s not a line a of symmetry. ❎

Let’s try a diagonal line like this:

Is it a line of symmetry?

Yes! ✅

This shape has 5 lines of symmetry. 

It is symmetrical. 😃

Good job! 🎉 Now, move on to the practice! It helps you remember for longer.

compositional balance, symmetry and asymmetry

A balanced composition seems right. It looks stable and aesthetically pleasing. Although some of its elements may stand out as focal points, no part draws the eye enough to overwhelm the rest. All elements are combined with each other, smoothly connecting with each other and forming a single whole.

Unbalanced composition causes tension. When a design is disharmonious, its individual elements dominate the whole, and the composition becomes less than the sum of its parts. Sometimes such disharmony can make sense, but more often than not, balance, order, and rhythm are the best solution.

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Physical and visual balance

It is easy to understand what balance is from the point of view of physics — we feel it all the time: if something is not balanced, it is unstable. Surely as a child you swung on a swing-board — you are on one end, your friend is on the other. If you weighed about the same, it was easy for you to balance on them.

The following picture illustrates the balance: two people of the same weight are at an equal distance from the fulcrum on which the swing is balanced.

Seesaw in symmetrical balance

The person on the right end of the board swings it clockwise, while the person on the left end swings it counterclockwise. They apply the same force in opposite directions, so the sum is zero.

But if one person were much heavier, the balance would disappear.

Unbalanced

This picture seems wrong because we know that the piece on the left is too small to balance the piece on the right, and the right end of the board must be touching the ground.

But if you move the larger piece to the center of the board, the picture will look more believable:

Seesaw in asymmetrical balance
The weight of the larger figure is offset by the fact that it is located closer to the fulcrum on which the swing is balanced. If you’ve ever been on a swing like this, or at least seen others doing it, then you know what’s going on.

Compositional balance in design is based on the same principles. The physical mass is replaced by a visual one, and the direction in which the force of gravity acts on it is replaced by a visual direction:

1. Visual mass is the perceived mass of a visual element, a measure of how much attention a given page element draws.

2. Visual direction is the perceived direction of the visual force in which we think an object would move if it could move under the influence of physical forces acting on it.

There are no tools to measure these forces, and no formulas to calculate visual balance: to determine if a composition is balanced, you rely only on your eyes.

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Why is visual balance important?

Visual balance is just as important as physical balance: an unbalanced composition makes the viewer feel uncomfortable. Look at the second seesaw illustration: it doesn’t seem right because we know the seesaw has to touch the ground.

From a marketing perspective, visual mass is a measure of the visual interest that an area or element on a page generates. When a landing page is visually balanced, every part of it creates some interest, and a balanced design keeps the viewer’s attention.

In the absence of visual balance, the visitor may not see some design elements — most likely, he will not look at areas that are inferior to others in visual interest, so that the information associated with them will go unnoticed.

If you want users to know everything you intend to tell them, consider developing a balanced design.

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Four types of balance

There are several ways to achieve compositional balance. The pictures in the section above illustrate two of them: the first is an example of a symmetrical balance, and the second is an example of an asymmetric one. The other two types are radial and mosaic.

1. Symmetrical balance

Symmetrical balance is achieved when objects of equal visual mass are placed at an equal distance from the fulcrum or axis at the center. Symmetrical balance evokes a sense of formality (which is why it is sometimes called formal balance) and elegance. A wedding invitation is an example of a composition that you most likely want to make symmetrical.

The disadvantage of symmetrical balance is that it is static and sometimes boring: if half of the composition is a mirror image of the other half, then at least one half will be quite predictable.

2. Asymmetric balance

Asymmetrical balance is achieved when objects on opposite sides of the center have the same visual mass. In this case, on one half there may be a dominant element, balanced by several less important focal points on the other half. Thus, a visually heavy element (red circle) on one side is balanced by a number of lighter elements on the other (blue stripes).

Asymmetric balance is more dynamic and interesting. It evokes a sense of modernity, movement, life and energy. Asymmetric balance is harder to achieve because the relationships between elements are more complex, but on the other hand it leaves more room for creativity.

3. Radial balance

Radial balance is achieved when elements radiate from a common center. The rays of the sun or the circles on the water after a stone has fallen into it are examples of radial equilibrium. Maintaining the focal point (fulcrum) is easy because it is always in the center.

The rays diverge from the center and lead to it, making it the most noticeable part of the composition.

4. Mosaic balance

Mosaic equilibrium (or crystallographic balance) is a balanced chaos, as in the paintings of Jackson Pollock. Such a composition does not have pronounced focal points, and all elements are equally important. The lack of hierarchy, at first glance, creates visual noise, but, nevertheless, somehow all the elements fit together and form a single whole.

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Symmetry and asymmetry

Both symmetry and asymmetry can be used in a composition, no matter what type of balance it is: you can use objects with a symmetrical shape to create an asymmetrical composition, and vice versa.

Symmetry is generally considered beautiful and harmonious. However, it can also seem static and boring. Asymmetry usually appears more interesting and dynamic, although not always beautiful.

Symmetry

Mirror symmetry (or bilateral symmetry) occurs when two halves of the composition, located on opposite sides of the central axis, are mirror images of each other. Most likely, when you hear the word «symmetry», you imagine exactly this.

The direction and orientation of the axis can be anything, although it is often either vertical or horizontal. Many natural forms that grow or move parallel to the earth’s surface are mirror-symmetric. Her examples are butterfly wings and human faces.

If the two halves of the composition reflect each other absolutely exactly, such symmetry is called pure. In most cases, the reflections are not completely identical, and the halves are slightly different from each other. This is incomplete symmetry — in life it is much more common than pure symmetry.

Circular symmetry (or radial symmetry) occurs when objects are arranged around a common center. Their number and the angle at which they are located relative to the center can be any — symmetry is preserved as long as there is a common center. Natural forms that grow or move perpendicular to the earth’s surface are circularly symmetrical, such as the petals of a sunflower. Alternation without reflection can be used to show motivation, speed, or dynamic action: imagine the spinning wheels of a moving car.

Translational symmetry (or crystallographic symmetry) occurs when elements are repeated at regular intervals. An example of this symmetry is repeated fence slats. Translational symmetry can occur in any direction and at any distance, as long as the direction is the same. Natural forms acquire this symmetry through reproduction. With translational symmetry, you can create rhythm, movement, speed, or dynamic action.

A butterfly is an example of mirror symmetry, a fence slat is translational, a sunflower is circular.

Symmetrical forms are most often perceived as figures against a background. The visual mass of a symmetrical figure will be greater than that of an asymmetrical figure of similar size and shape. Symmetry creates balance on its own, but it can be too stable and too calm, uninteresting.

Asymmetry

Asymmetrical shapes don’t have the same balance as symmetrical ones, but you can balance the whole composition asymmetrically. Asymmetry often occurs in natural forms: you are right-handed or left-handed, tree branches grow in different directions, clouds take on random shapes.

Asymmetry leads to more complex relationships between the elements of a space and is therefore considered more interesting than symmetry, which means it can be used to draw attention.

The space around asymmetrical shapes is more active: patterns are often unpredictable, and overall you have more freedom to express yourself. The flip side of asymmetry is that it’s harder to balance.

You can combine symmetry and asymmetry and achieve good results — create a symmetrical balance of asymmetrical shapes and vice versa, break up a symmetrical shape with a random label to make it more interesting. Collide symmetry and asymmetry in the composition so that its elements attract more attention.

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Principles of Gestalt Psychology

Design principles do not emerge from nothing: they follow from the psychology of our perception of the visual environment. Many design principles grow out of the principles of Gestalt psychology and also build on each other.

So, one of the principles of Gestalt psychology concerns precisely symmetry and order and can be applied to compositional balance. However, this is perhaps the only principle applicable to it.

Other principles of Gestalt psychology, such as focal points and simplicity, add up to the visual mass, and the good continuation factor, common destiny factor, and parallelism set the visual direction. Symmetrical forms are most often perceived as figures against a background.

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Examples of different approaches to web design

It’s time for real examples. The landing pages below are grouped into four types of balance. Perhaps you will perceive the design of these pages differently, and that’s good: critical thinking is more important than unconditional acceptance.

Examples of symmetrical balance

The Helen & Hard website design is symmetrical. The About Us page in the screenshot below and all other pages on this site are balanced in a similar way:

Screenshot of the Helen & Hard About Us page

All elements located on opposite sides of the vertical axis located in the center of the page mirror each other. Logo, navigation bar, round photos, title, three columns of text — centered.

However, the symmetry is not perfect: for example, columns contain different amounts of text. By the way, look at the top of the page. Both the logo and the navigation bar are centered, but visually they don’t appear to be centered. Maybe the logo should have been centered on the ampersand, or at least the area next to it.

The three menu text links located on the right side of the navigation bar have more letters than the links on the left side — it seems that the center should be between About and People. Maybe if these elements were not really centered, but visually centered, the whole composition would look more balanced.

The Tilde homepage is another example of symmetrical balance design. Like on Helen & Hard, everything is arranged around a vertical axis running down the center of the page: navigation, text, people in photos.

Tilde homepage screenshot

As in the case of Helen & Hard, the symmetry is not perfect: firstly, the centered lines of text cannot be a reflection of the photograph from below, and secondly, a couple of elements stand out from the general row — the “Meet the Team” arrow points to the right, and the text at the bottom of the page ends with another right arrow. Both arrows are calls to action and both break the symmetry, drawing additional attention to themselves. In addition, the color of both arrows contrast with the background, which also attracts the eye.

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    Carrie Voldengen’s homepage showcases an asymmetrical balance around a dominant symmetrical shape. Looking at the composition as a whole, several separate shapes can be seen:

    Carrie Voldengen website screenshot

    Most of the page is occupied by a rectangle consisting of a grid of smaller rectangular images. The grille itself is symmetrical in both the vertical and horizontal axes and appears to be very solid and stable — you could even say that it is too balanced and looks immovable.

    The block of text on the right breaks the symmetry. The lattice is contrasted with text and a round logo in the upper left corner of the page. These two elements have approximately equal visual mass acting on the grating from different sides. The distance to the imaginary fulcrum is about the same as the mass. The block of text on the right is larger and darker, but the round blue logo adds weight to its area and even matches the top left corner of the grid in color. The text at the bottom of the grid seems to hang from it, but it is light enough not to disturb the compositional balance.

    Notice how the white space also seems to be balanced. The voids on the left, top and bottom, as well as on the right under the text — balance each other. There is more white space on the left side of the page than on the right side, but there is extra space on the right side at the top and bottom.

    The images in the header of the Hirondelle USA page change from one to another. The screenshot below was taken specifically to demonstrate the asymmetric compositional balance.

    Screenshot Hirondelle USA

    The column in the photo is off-center slightly to the right and creates a noticeable vertical line because we know the column is a very heavy object. The railing on the left creates a strong connection to the left edge of the screen and feels solid enough too.

    The text above the railing seems to rest on it; in addition, on the right it is visually balanced by a photograph of a boy. It may seem that the railing seems to be hanging from the column, upsetting the balance, but the presence of the boy and the darker background behind him balance the composition, and the light text restores the balance as a whole.

    The gold colored links in the upper left and lower right corners create a sense of translational symmetry, as does the button at the bottom of the page. The white text is also repeated.

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    Examples of radial balance

    The homepage of Vlog.it demonstrates radial balance, as seen in the screenshot. Everything but the object in the upper right is organized around the center, and the three rings of images rotate around the center circle.

    Screenshot of Vlog.it home page

    However, the screenshot does not show how the page loads: a line is drawn from the lower left corner of the screen to its center — and from that moment on, everything that appears on the page rotates around the center or radiates from it, like circles on water.

    The small circle in the upper right corner adds translational symmetry and asymmetry, increasing visual interest in the composition.

    Opera’s Shiny Demos home page doesn’t have circles, but all the text links radiate from a common center, and it’s easy to imagine the whole structure rotating around one of the central squares, or maybe one of the corners:

    Screenshot of Opera’s Shiny Demos homepage

    The name Shiny Demos in the top left and the Opera logo in the bottom right balance each other out and also seem to emanate from the same center as the text links.

    This is a good example that it is not necessary to use circles to achieve radial balance.

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    Examples of mosaic equilibrium

    You might think that mosaic balance is the least used on websites, especially after the paintings of Jackson Pollock were cited as an example. But mosaic equilibrium is much more common than it seems.

    A prime example is the home page of Rabbit’s Tale. Letters scattered across the screen definitely create a sense of chaos, but the compositional balance is there.

    Screenshot of Rabbit’s Tale homepage

    Almost equal in size areas of color and space, located on both sides, on the right and on the left, balance each other. The rabbit in the center serves as a fulcrum. Each element does not attract attention on its own.

    It is difficult to figure out which specific elements balance each other, but in general there is a balance. Maybe the visual mass on the right side is a little bigger, but not enough to upset the balance.

    Sites with a lot of content, such as news portals or magazine sites, also exhibit tiled balance. Here is a screenshot of The Onion homepage:

    Screenshot of The Onion homepage

    There are a lot of elements, their arrangement is not symmetrical, the size of the text columns is not the same, and it is difficult to understand what balances what. Blocks contain different amounts of content, and hence their sizes vary. Objects are not located around some common center.

    Blocks of varying sizes and densities create a somewhat cluttered feel. Since the site is updated every day, the structure of this chaos is constantly changing. But overall, the balance is maintained.

    You might consider this example of tiled balance far-fetched, but many sites organize their content this way. Although, probably, most of the mess is not planned on purpose.

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    Conclusion

    Design principles draw heavily from Gestalt psychology and perceptual theory and are based on how we perceive and interpret our visual environment. For example, one of the reasons we notice focal points is because they contrast with the elements around them.

    However, design principles are not hard and fast rules that must be followed, but rather guidelines. So, there is no single way to accurately determine the visual mass of an object. You are not required to unconditionally follow all the techniques described above, but it would be nice to understand them, if only in order to break the rules consciously.

    High conversions for you!

    Source: smashingmagazine.com. image source dmcwa

    11-11-2015

    Symmetrical shape — The Great Encyclopedia of Oil and Gas, article, page 3

    Page 3

    half of the full image.
    [31]

    When drawing details of of the symmetrical shape of , it is also possible to draw a part of its view, slightly exceeding half of the full image.
    [32]

    Triangle it is desirable to arrange a symmetrical shape with a straight base.
    [33]

    The hypothesis of the transition from the symmetrical form of hydrocarbon to the asymmetric intermediate is based on the uneven stability of the methyl groups with respect to attacking oxygen.
    [34]

    Energy profile of C-C rotation — bonds in ethane.
    [35]

    In one of the 9In the 0357 symmetric form of the conformer, the hydrogen atoms are in an eclipsed position, while in the other symmetrical form, the hydrogen atoms are staggered relative to the central bond. On fig. 2.1.2 also shows the effect of a complete rotation around the central bond on the potential energy.
    [36]

    If the wing has a symmetrical shape in plan and moves without sliding, then the flow pattern around the wing is symmetrical with respect to the plane O. Therefore, we consider the right side of the wing, and take into account the effect of the left side on the basis of the symmetry condition.
    [37]

    If the body has a symmetrical shape (fig. 10.23 shows the cross section of the ball), then the flow will be symmetrical. In this case, there is no frontal resistance. In real conditions, due to friction in the gas, some redistribution of streamlines occurs, the flow around becomes asymmetric, and this leads to the appearance of aerodynamic forces.
    [38]

    If the product has a symmetrical shape and the axis of symmetry is marked on the drawing, it is allowed to mark with leader lines and designate seams only on one of the symmetrical parts of the product.
    [39]

    If the section has a symmetrical shape and is located in the gap between the parts of the part itself (Fig. 4.26), then the section line is not marked with letters and the section is not inscribed.
    [40]

    Aim for the symmetrical shape of part with respect to the parting plane and symmetrical slopes of the projecting walls (Fig.

By alexxlab

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