homework of symmetry

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Symmetry Worksheets

Symmetry worksheets consist of a variety of skills for children in grade 1 through grade 5 to understand the lines of symmetry in different shapes. Printable exercises to identify and draw the lines of symmetry, complete the shapes, count the lines of symmetry in each shape, to identify symmetrical or asymmetrical shapes and to determine the perimeter of shapes are given here for practice. Begin your practice with our free symmetry worksheets!

Recognizing Lines of Symmetry

Each symmetry worksheet pdf here shows eight different shapes through which a dotted line is drawn. Identify if the dotted line is a line of symmetry.

• Download the set

Drawing a Line of Symmetry: Shapes

Three exclusive worksheets to identify and draw a line of symmetry on each shape are given here.

Drawing a Line of Symmetry: Real-Life Objects

Draw a line of symmetry for each real-life objects. Some objects may have more than one line of symmetry.

Lines of Symmetry: More than One Line

Shapes with more than one line of symmetry are given in these pdf worksheets. Determine and draw lines of symmetry on each shape and write down the number of lines of symmetry seen.

Complete the Mirror Image: Standard

One-half of symmetrical shapes are shown. Task grade 2 and grade 3 kids to draw the other half of the mirror image.

Complete the Mirror Image: Grid

One-half of real-life objects are drawn in the grids. Complete the second half of each symmetrical shape and solve the pdf worksheets.

Cut-Paste Activity: Symmetric / Asymmetric

Cut out each shape from the bottom of these printable worksheets for 1st grade and 2nd grade kids and paste them in the appropriate category (symmetric or asymmetric shapes).

Cut-Paste Activity: Complete the Shape

A symmetrical half of the shapes are shown. The other half of each shape is given below. Cut out the other half and paste them to complete the shape.

Symmetry on English Letters

Grade 4 children identify if the English letters shown are cut at the line of symmetry in part 1. Draw lines of symmetry on the given English letters in part 2.

Unfold the Mystery

Each folded paper has a cutout region. Choose the exact shape obtained at the center when the paper is unfolded.

Perimeter of Symmetrical Shapes

Each printable worksheet shows eight symmetrical shapes with all the possible lines of symmetry. Students in 3rd grade, 4th grade, and 5th grade need to find the perimeter of each symmetrical shape using the information given.

Related Worksheets

» Slide, Flip and Turn

» Rotation

» Translation

» Reflection

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Symmetry Worksheets Line Symmetry Easier

Welcome to the Math Salamanders Line Symmetry Worksheets page. Here you will find a range of free printable symmetry worksheets, which will help your child to practice their reflecting and flipping skills.

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Symmetry Help

The Math Salamanders have a large bank of free printable symmetry worksheets. Each symmetry sheet comes complete with answers for support.

Handy Hints

Each point or block that has been reflected must remain the same distance from the mirror line as the original point. So if point A is 3 squares away from the mirror line, then the reflection of point A must also be 3 squares away.

When reflecting a shape, look at the corners of the shape and reflect each corner first as a dot in the mirror line. The dots can then be joined up (in the correct order!)

For lines of symmetry at angles of 45°, it is often better to rotate your paper so that the line of symmetry is vertical or horizontal, and the rest of the paper is at an angle.

The basis and understanding of symmetry starts at about Grade 2, and then develops further in Grades 3,4 and 5.

Line Symmetry Worksheets

On this webpage you will find our range of line symmetry sheets for kids.

The sheets have been carefully graded with the easier sheets coming first. The first 3 worksheets involve only horizontal and vertical lines only. The next 3 worksheets involve reflecting diagonal lines as well.

There are also some templates at the end of this section for you to create your own shapes for your child to reflect, or, even better, for your child to create their own symmetric patterns!

Using these sheets will help your child to:

• learn to reflect a shape in a vertical or horizontal mirror line;
• learn to reflect a shape in both a vertical and horizontal mirror line;

Reflecting in 1 mirror line

Horizontal and vertical lines only.

• Line Symmetry 1
• PDF version
• Line Symmetry 2
• Line Symmetry 3
• Line Symmetry 4
• Line Symmetry 5
• Line Symmetry 6

Reflecting in Diagonal mirror lines

• Line Symmetry 9
• Line Symmetry 10

Reflecting in vertical, horizontal and diagonal lines

• Line Symmetry 11

Reflecting in 2 mirror lines

• Line Symmetry 7
• Sheet 7 Answers
• Line Symmetry 8
• Sheet 8 Answers

Reflecting in vertical and horizontal or 2 diagonal lines

• Line Symmetry 12

Line Symmetry templates

• Line Symmetry Template 1
• Line Symmetry Template 2
• Line Symmetry Template 3
• Line Symmetry Template 4
• Line Symmetry Template 5
• Line Symmetry Template 6

Looking for something harder?

Here you will find a range of line symmetry activity sheets with one or two mirror lines.

The sheets in this section are similar to those on this page, but are more complicated and at a harder level.

• Harder Symmetry Activities

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Block Symmetry Worksheets

Here you will find a range of symmetry worksheets reflecting blocks instead of lines.

These sheets are at an easier level than the ones on this page.

• Symmetry Worksheets - Block Symmetry
• Explore 2d Shapes Worksheets

Looking for some geometry worksheets to get children thinking and reasoning about 2d shapes?

The shapes on this page are all about children really understanding what 2d shapes are all about, and using their reasoning skills to justify their thinking.

• know the properties of a range of 2d shapes;
• recognise that some shapes can also be described as being other shapes; e.g. a square is also a rhombus;
• recognise and understand right angles, parallel lines, lines of symmetry;
• develop their geometric reasoning skills.

Coordinate Sheets

Here is our collection of printable coordinate plane grids and coordinate worksheets.

Using these fun coordinate sheets is a great way to learn math in an enjoyable way.

• plot and write coordinates.
• Coordinate Plane Grid templates
• Coordinate Worksheets (1st Quadrant)
• Coordinate Plane Worksheets (All 4 Quadrants)

Captain Recommends

Have a look at these online symmetry games - a great way to learn symmetry and get instant feedback!

• Softschools Symmetry Game
• Sheppard Software Symmetry Activities

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Lines of Symmetry

Lines of symmetry

Here you will learn about lines of symmetry, including symmetry properties within polygons, angle properties, and symmetry of different line graphs.

Students first learn about line symmetry in grade 4 with their work with 2D shapes in geometry.

What are lines of symmetry?

Lines of symmetry are straight lines that divide a shape into two equal parts, where one part is an exact reflection or mirror image of the other.

In geometry, many 2D shapes have line symmetry.

For example,

Line symmetry can be seen in nature.

Line symmetry can be seen in art.

Lines of symmetry in regular shapes

Regular polygons are polygons that have equal side lengths and equal angle measures. 

Notice how the number of lines of symmetry in these regular polygons is equal to the number of sides and angles the polygons have.

All regular polygons share the property that the number of sides is equal to the number of lines of symmetry.

[FREE] 2D Shape Worksheet (Grade 2 to 4)

Use this quiz to check your grade 2 – 4 students’ understanding of 2D shape. 10+ questions with answers covering a range of 2nd, 3rd and 4th grade 2D shape topics to identify areas of strength and support!

Lines of symmetry in irregular shapes

Irregular polygons are polygons that do not have all equal angles and all equal side lengths. However, they can have line symmetry.

For example, these irregular polygons have line symmetry.

Let’s look at different shapes (specifically quadrilaterals) and their number of lines of symmetry.

Lines of symmetry in circles

The diameter of a circle splits the circle into two equal sized half circles, or semicircles. Think of the diameter as the line of reflection.

A circle can be folded in-half many ways, meaning that there are an infinite number of lines of symmetry. 

Common Core State Standards

How does this apply to 4th grade math?

• Grade 4: Geometry (4.G.A.3) Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

How to identify lines of symmetry

In order to draw/identify lines of symmetry:

Locate the center of the 2D shape.

Draw a vertical line through the center and check for line symmetry.

Draw a horizontal line through the marked center and check for line symmetry.

• Draw a line from each vertex through the center and check for symmetry.

State the number of lines of symmetry.

Lines of symmetry examples

Example 1: regular shapes.

How many lines of symmetry does the equilateral triangle have?

2 Draw a vertical line through the center and check for line symmetry.

The vertical line through the center is a line of symmetry dividing the triangle into two equal halves that are mirror images of each other. Notice that it can be a fold line.

3 Draw a horizontal line through the marked center and check for line symmetry.

4 Draw a line from each vertex through the center and check for line symmetry.

5 State the number of lines of symmetry.

The equilateral triangle has 3 lines of symmetry. An equilateral triangle has 3 equal sides and 3 equal angles, so it will have 3 lines of symmetry.

Example 2: the regular pentagon

How many lines of symmetry does the regular pentagon have?

The vertical line is a line of symmetry because it divides the regular pentagon into two equal halves that are mirror images of each other.

The horizontal line is NOT a line of symmetry because it does not divide the regular pentagon into two equal halves that are mirror images of each other.

Draw a line from each vertex through the center and check for line symmetry.   

A regular pentagon has 5 lines of symmetry. A regular pentagon has 5 equal sides and 5 equal angles, so it will have 5 lines of symmetry.

Example 3: irregular shapes

How many lines of symmetry does the trapezoid have?

The vertical line is a line of symmetry because it divides the trapezoid into two equal halves that are mirror images of each other.

The horizontal line is NOT a line of symmetry because it does not divide the trapezoid into two equal halves that are mirror images of each other.

The trapezoid has one line of symmetry.

Example 4: irregular shapes

How many lines of symmetry does the irregular hexagon have?

The vertical line is a line of symmetry because it divides the irregular hexagon into two equal halves that are mirror images.

The horizontal line is a line of symmetry because it divides the irregular hexagon into two equal halves that are mirror images.

The irregular hexagon has two lines of symmetry.

Example 5: irregular shapes

How many lines of symmetry does the parallelogram have?

The vertical line is NOT a line of symmetry because it does not divide the parallelogram into two equal halves that are mirror images of each other.

The horizontal line is NOT a line of symmetry because it does not divide the parallelogram into two equal halves that are mirror images of each other.

The parallelogram does not have any lines of symmetry.

Example 6: irregular shapes

How many lines of symmetry does the shape have?

The vertical line is a line of symmetry because it divides the shape into two equal halves that are mirror images of each other.

The horizontal line is a line of symmetry because it divides the shape into two equal halves that are mirror images of each other.

The irregular shape has 4 lines of symmetry.

Teaching tips for lines of symmetry

• Use hands on manipulatives to help students gain understanding of lines of symmetry.
• Infuse creative activities such as origami so that students can build understanding through fun learning tasks.

Easy mistakes to make

• Thinking that all quadrilaterals have \bf{4} lines of symmetry The only quadrilateral with 4 lines of symmetry is a square because it is a regular polygon. The other quadrilaterals are not regular polygons so do not have 4 lines of symmetry.
• The number of sides always \textbf{=} the number of lines of symmetry Although this is true for regular shapes, it is not true for all shapes.

Related symmetry lessons

• Rational symmetry

Practice lines of symmetry questions

1. Find the number of lines of symmetry for the regular hexagon below.

Regular polygons have the same number of lines of symmetry as the number of sides that they have.

A hexagon has 6 sides so it has 6 lines of symmetry.

Marking the center, there are 6 lines that can be drawn through the center that cut the regular hexagon into equal halves that are mirror images of each other.

2. Find the number of lines of symmetry for the rectangle below.

After marking the center, the vertical line through the center and the horizontal line through the center are the only lines of symmetry.

Any other line drawn through the center will not result in the shape being divided into two equal halves that are mirror images.

3. Find the number of lines of symmetry for the kite below.

After marking the center, the only line of symmetry is the horizontal line.

There is no other line that can be drawn through the center that will divide the shape into two equal parts that are mirror images of each other.

4. Find the number of lines of symmetry for the irregular hexagon below.

After marking the center, the lines of symmetry are the vertical line through the center and the horizontal line through the center.

No other lines through the center will divide the shape into two equal parts that are mirror images of each other.

5. How many lines of symmetry does the smiley have?

Circles have an infinite amount of lines of symmetry. However, you have to take the eyes and mouth into account when figuring out the lines of symmetry.

There is only one line of symmetry vertically down the face that will divide the smiley face into two equal mirror images of each other.

6. How many lines of symmetry does the photo have?

The photo has two lines of symmetry, one that is horizontal through the center and the other that is vertical through the center.

There are no other lines that can be drawn that divides the photo into two equal halves that are mirror images of each other.

Lines of symmetry FAQs

There are two types of symmetry. Line symmetry is drawing a line through the center of a figure where both halves are mirror images of each other. Rotational symmetry involves turning a shape and determining how many times the shape appears as its original in one complete 360^{\circ} turn.

In algebra, you will learn about quadratic functions whose graph is a parabola. The parabola has a line going through the center that divides it into identical halves, which is the axis of symmetry. It is also the line of symmetry of the parabola.

No, a scalene triangle does not have any lines of symmetry. Meaning there are no imaginary lines or mirror lines that can be drawn through the center of the triangle, where one half is equal and the mirror image of the other half. Isosceles triangles have only one line of symmetry. Equilateral triangles are regular polygons, so they have 3 lines of symmetry.

Yes, regular polygons are symmetrical shapes because they have equal sides and equal angles. They have line symmetry and rotational symmetry.

Congruent means identical in shape and size. When drawing a dotted line representing line symmetry, each half of the shape is congruent.

The next lessons are

• Angles in polygons
• Congruence and similarity
• Transformations

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Symmetry Worksheets

Printable practice worksheets to help you teach and review symmetry.  Includes worksheets the require students to draw lines of symmetry, determine which pictures are symmetrical, and design symmetrical illustrations.

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Learn about lines, angles, polygons, solid shapes, circles, and more!

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7 Superb Symmetry Activities (with a FREEBIE!)

• Freebies , Math , Planning

In the hustle and bustle of the upper elementary classroom, where every moment is precious and every standard is vital, it can be difficult to give every last educational concept the attention it deserves. This is especially true when a concept only has one or two standards addressing it. If it only has one standard in all of upper elementary, then it must not be too important, right?

… Or, maybe, the concept is just SO important that it only needs to be covered once to make a lasting impact on your kiddos! That’s what I’m choosing to believe, anyway, when it comes to symmetry. Maybe it’s my artistic side speaking, but I absolutely LOVE symmetry, and it actually hurts my feelings that this geometry concept doesn’t always get the attention it deserves.

For instance, when conducting my research for this blog post, I noticed a severe lack of educational resources and ideas that align with the Common Core State Standard 4.G.3 : “Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.”

It’s obviously important to ensure your kiddos are meeting CCSS, but once that goal is met, symmetry can sometimes fall to the wayside. It’s understandable, since there are simply SO MANY standards to get to, but symmetry really is important in its own right!

Let’s check out why it’s vital to students’ mathematical careers, then we’ll dive into seven symmetry activities that are sure to supplement your geometry lessons… Complete with a FREEBIE at the end!

Why Bother with Symmetry?

It’s not just important to cover symmetry in preparation for testing. Exploring symmetry helps students build fluency in math by reinforcing key concepts like congruence, transformations, and geometric properties. By working through engaging, hands-on symmetry activities and discussions, students develop a stronger understanding of math principles and develop fluency in applying them to new situations.

In addition, building a strong foundation in symmetry also helps students develop spatial reasoning skills, which are super important for understanding tougher geometric concepts and spatial relationships down the line. It’s a great way to help students learn to visualize shapes, identify patterns, and make predictions.

There’s also plenty of symmetry to be found in nature, too! This is certainly a neat way to make real-world connections with your kiddos, but beyond that, it also provides you with a great opportunity for an integrated curriculum with Earth science… Which, as you know, is like, my favorite thing ever . 😉

Okay, I think I’ve made my point. Let’s jump right into the activities!

Seven Symmetry Activities

1. symmetry art swap.

For this activity, you’ll want to provide individuals with graph paper and art supplies. Every student will begin by creating a “line of symmetry,” preferably horizontal or vertical to begin with, through the center of the page. Then, they can create a geometric design of their liking on ONE side of the mirror line. Of course, students should be given free agency with their designs, but you may want to encourage simpler designs to start with to allow kiddos to get the hang of the concept of symmetry.

Once students have created their designs on one side of the mirror line, have them swap their graph paper with a partner. The partner should then try to finish the design on the other side of the symmetry line! Since this is a pretty quick activity, I recommend having students repeat these steps a few more times. They can experiment with more complex designs and even add colors to be mirrored!

It’s not a bad idea either to encourage kiddos to find NEW partners every time, too. You don’t want them sticking to only their best friend—switch it up so everyone gets a diverse experience.

These symmetry art pieces can be shown off in the classroom or even a hallway bulletin board for a cute, easy display. Kiddos love showing off their work, and a splash of color in the halls always does wonders to brighten spirits!

2. Symmetry Manipulatives

Similar to the art swap above, this is another way for students to express their creativity by creating symmetrical designs. This time, though, they can only use manipulatives, such as pattern blocks, tangrams, or other physical geometrical shapes. It’s a bit more challenging than the art swap, since they don’t have complete freedom over the design; rather, they’re bound by the dimensions of the trapezoids and rhombuses and squares!

For this activity, have students sit across from one another and try to replicate one another’s designs using the pattern blocks. They should notice that the design is “mirrored” across a horizontal line of symmetry between them. Kiddos can even take turns making designs and creating a symmetrical version.

3. Symmetry Construction

If someone had told me back at university just how much I’d end up advocating for the use of toothpicks in the classroom, I would never have believed them… But, goodness, there’s no denying their myriad of uses! From fencing in animals to investigating camouflage , toothpicks are practically the backbone of hands-on activities.

And, as you’re sure to see, geometry is no exception! For this activity, have students use toothpicks to create symmetrical shapes. They can connect the toothpicks (or even popsicle sticks, if you prefer) at their endpoints to form geometric shapes, then identify and label the lines of symmetry within their creations—or you can have a partner do that part.

Challenge students to see how many lines of symmetry they can create within one design! Of course, in that case, you may want to ban circles… That might be a little too easy. 😉

4. Symmetry Scavenger Hunt

Listen, I know I recommend scavenger hunts, like, ALL the time, but you can’t blame me: they’re a perfect way to get students up and moving around, keeping them engaged while staying on-task!

For this activity, you’ll encourage kiddos to engage with a geometric scavenger hunt around the classroom, encouraging them to search for symmetrical objects or patterns. If you’d like, you can set out symmetrical pictures or the like ahead of time, but that’s not totally necessary; most classrooms are already chock-full of symmetry if you take the time to look!

Have students record their findings in a notebook or on a piece of paper as they move through the scavenger hunt. They should sketch all of the items they discover that are symmetrical and draw its lines of symmetry—for instance, they could draw the top-down view of a desk and include all of its symmetrical lines.

Once students have had enough time to scan the entire room, reconvene as a class and discuss their findings. Encourage productive discussion by asking questions, such as “Which objects have the most symmetrical lines?” and even deeper critical-thinking questions like “Would the entire classroom be symmetrical if it were mirrored? Why or why not?”

5. Symmetry Nature Walk

What’s this? Another opportunity to integrate curriculum? You got it! Add a helping of Earth science to your geometry unit by bringing students outside to make mathematical observations about nature.

Before heading outside, however, it’s time for a brainstorm sesh. As a class, discuss what kinds of symmetrical objects you may find outside! This is a good way to get students visualizing symmetry, which is a vital step to fully grasping geometry.

Then… Go outside! Just like with the scavenger hunt, have kiddos bring along paper in order to sketch images of the symmetrical objects they find along with their lines of symmetry. Some common examples they may find outside are leaves, flowers, and even insects!

After the adventure, reconvene in the classroom and have students share their findings. Ask more questions, like which objects outside had the most lines of symmetry, if there were any perfectly symmetrical objects (like circles) and so on.

This is a great opportunity for critical thinking, too! What observations can your students make about symmetry in nature? Is it common? Lots of wildlife is symmetrical to some degree, like humans. Why do they think this is? There are no right or wrong answers; the exercise is simply meant to get students thinking and visualizing!

6. Symmetry Stations

Next up, set up several different stations around the room that each center around a type of geometric shape, such as circles and ovals, triangles, parallelograms, and other shapes, like hearts, crosses, arrows, stars, and so on.

Each station should have around five “cards” each that have a different shape relevant to the station’s theme. For example, the triangle station should feature five different triangles of different sizes, each with varying amounts of lines of symmetry.

At each station, students should sketch the shapes on the cards on their own personal graph paper. Then, they can fold their paper to find lines of symmetry! The folding is an important part—not just because it’s hands-on, but also because it ensures that students are fully grasping the concept, specifically as it’s cited in CCSS 4.G.3 : “Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.”

Students should work together with groups or partners and go through all of the stations until they have “dissected” all of the cards at each center. Then, go over the answers as a class and discuss any questions or thoughts your kiddos may have.

7. Symmetry Assessment Activities

Now that your students have explored the nuances of symmetry, it’s time to check for understanding! Let’s start with a couple informal assessments .

Ticket-out-the-doors are a great method here, as you can simply draw half of a shape on the whiteboard and have students copy that shape onto a piece of scrap paper. Then, they would finish drawing its other side, taking care to keep the shape symmetrical. Once they turn in the paper, you can easily see right off the bat who has grasped the concept and who may still need a bit more help to properly visualize symmetry.

Another informal assessment to use here is Four Corners. Assign each corner of your classroom a number, one through four. This number will represent the lines of symmetry that a shape has. Then, draw a shape on the whiteboard and have students move to whichever corner of the room matches the number of lines of symmetry they think the shape has.

It’s definitely a plus to get students up and moving around, but if you’re pressed for time, no worries! Instead of using Four Corners, you can simply draw the shape on the whiteboard, then have your students raise up the number of fingers that match how many lines of symmetry the shape has.

If you’re finding your kiddos can still use a bit of practice, or if you just want to incorporate some review time, I’ve got you covered: check out this symmetry FREEBIE pulled straight from my fourth grade math workshop geometry unit! Click the pic below or the link above to download the worksheet. And, hey, if you like that, then you can find the full 4th Grade Math Workshop Geometry Unit here !

With this array of ideas to choose from, you and your kiddos are ready to grab your compass, sharpen your pencils, and take off on an adventure of symmetry! Don’t let this math concept just be an addendum to your geometry unit; give symmetry the attention it deserves in your upper elementary classroom.

And, as always, be on the lookout for more engaging, easy-to-implement ideas for your math and science students. While you’re here, sign up for my email list so you won’t miss out!

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Lines of Symmetry (Grade 4)

Suggested learning targets.

• I can identify shapes with symmetry.
• I can define symmetry.
• I can draw a line of symmetry.

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Reflection Symmetry

The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry ). It is easy to see, because one half is the reflection of the other half.

The reflection in this lake also has symmetry, but in this case:

• the Line of Symmetry runs left-to-right
• it is not perfect symmetry, as the image is changed a little by the lake surface.

The Line of Symmetry can be in any direction (not just up-down or left-right). To learn more, go to Reflection Symmetry .

Rotational Symmetry

With Rotational Symmetry , the image is rotated (around a central point) so that it appears 2 or more times. How many times it appears is called the Order .

Here are some examples (they were made using Symmetry Artist , and you can try it yourself!)

Point Symmetry

Point Symmetry is when every part has a matching part:

• the same distance from the central point
• but in the opposite direction.

It is also the same as "Rotational Symmetry of Order 2" above

Symmetry is often in art, for example Rangoli is a type of art common in India:

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Symmetry Worksheets

Updated:  06 Sep 2023

Use this set of eight symmetry worksheets to help students understand symmetry, the line of symmetry, and symmetrical objects.

Editable:  Google Slides

Non-Editable:  PDF

Pages:  2 Pages

• Curriculum Curriculum:  CCSS, TEKS

Grades:  4 - 6

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Symmetry Worksheets: Symmetry Art

The perfect way to explore symmetry is here! These symmetry worksheets are perfect for developing a student’s knowledge and understanding of lines of symmetry. Help students grasp this concept by showing them these shapes which, when ‘folded’ along their lines of symmetry, can be mirrored on the other side of the page.

These fun math worksheets allow students to use their critical thinking skills to complete the second half of a picture (the first half is already on the page for them!), following a grid on the page.

Encourage students to study the half-done drawing on the worksheet and imagine that a line running through the middle of the paper will split the drawing into two equal parts. Then your students can fill in the matching grid squares to create a reflection of the given pattern. This will reveal a mystery picture.

Symmetrical designs included in this pack are:

• Happy Face Emoji

Teacher tip: Teaching a theme? Perhaps it’s Halloween and you could use the Spider design to liven up your lessons! The Castle design would work well when teaching about fairytale narratives. The options for using this maths resource in your thematic unit are many!

Using these Symmetry Worksheets

Wondering how to get these fantastic symmetry worksheets into your busy planner? Why not:

• Include them as a math center or rotation activity
• Print some off and have them at hand in your fast-finisher box
• Send one home for a fun homework activity
• Set students the challenge of creating the most colorful design during Math class
• Use these as a mindful brain-break activity. Put on some quiet music and allow students to color and reflect at the same time.

Looking for more Symmetry Activities for Your Kids? We Have You Covered:

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2-D Shape Bingo

Engage your students while consolidate learning about 2D shapes, their names and properties with 2D Shape Bingo!

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We're Going On a Shape Hunt! Graphing Game

Consolidate students' knowledge of 2D shapes while teaching about data collection, recording and graphing!

Drawing 2-D Shapes Worksheet

A worksheet asking students to draw specific 2-D shapes.

In our Symmetry lesson plan, students learn all about symmetry, including how it’s defined and how to determine if something is symmetrical. Students practice drawing lines of symmetry, identifying symmetric figures, and drawing a symmetrical second half for various figures.

Description

Additional information.

Our Symmetry lesson plan enables students to define symmetry, recognize a line of symmetry for a two-dimensional figure, identify line-symmetric figures and draw lines of symmetry. Engage critical thinking and generalize understanding as students explore the ways the human body is symmetrical and the reasons why it does not have perfect symmetry. During this lesson, students are asked to complete a fun, interactive activity in which they cut out shapes and fold them to find lines of symmetry, recording the number of lines of symmetry they can find for each shape. Students are also asked to circle letters which are symmetrical, draw a symmetrical other half of pictures and more.

At the end of the lesson, students will be able to define symmetry, recognize a line of symmetry for a two-dimensional figure, identify line-symmetric figures, and draw lines of symmetry.

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Practical and fun worksheets

This resource is ready to go and provides some simple practical and informative worksheets for classes.

Worked well

It worked great for my lesson.

Simple Symmetry

I really liked the material and activities provided in the Symmetry lesson. The shape activity allowed for hands-on experience in understanding line symmetry. The homework made my students open their eyes to examples of symmetry that they could find in their own homes and neighborhoods. The only issue I had, was with the answer key. The answer key appears to have included rotational symmetry in their answers for the shapes, but didn't mention rotational symmetry in the student instructions. My students were busily folding the shapes and didn't know to investigate rotational symmetry as well. Otherwise, a great product!

Great resources, thank you

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Symmetry And Line Of Symmetry: An Introduction

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 .

If an object is symmetrical, it means that it is equal on both sides. Suppose, if we fold a paper such that half of the paper coincides with the other half of the paper, then the paper has symmetry. 

Symmetry can be defined for both regular and irregular shapes. For example, a square is a regular (all sides are equal) and a rectangle is an irregular shape (since only opposite sides are equal). The symmetries for both shapes are different. Check different figures with symmetry here.

Symmetry in Mathematics

In Mathematics, a meaning of symmetry defines that one shape is exactly like the other shape when it is moved, rotated, or flipped. Consider an example, when you are told to cut out a ‘heart’ from a piece of paper, don’t you simply fold the paper, draw one-half of the heart at the fold and cut it out to find that the other half exactly matches the first half? The heart carved out is an example of symmetry.

Symmetry Math definition states that “symmetry is a mirror image”. When an image looks identical to the original image after the shape is being turned or flipped, then it is called symmetry. It exists in patterns. You may have often heard of the term ‘symmetry’ in day to day life. It is a balanced and proportionate similarity found in two halves of an object, that is, one-half is the mirror image of the other half. And a shape that is not symmetrical is referred to as asymmetrical. Symmetric objects are found all around us, in nature, architecture, and art.

Symmetrical Figures

Symmetrical shapes or figures are the objects where we can place a line such that the images on both sides of the line mirror each other.  The below set of figures form symmetrical shapes when we place a plane or draw the lines.

For example, figure (b) has the symmetrical figures when we draw two lines of symmetry as shown below.

Line of Symmetry

The imaginary line or axis along which you fold a figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into two mirror-image halves. The line of symmetry can be vertical, horizontal or diagonal. There may be one or more lines of symmetry.

1 Line Symmetry

Figure is symmetrical only about one axis. It may be horizontal or vertical. The word ATOYOTA has one axis of symmetry along the axis passing through Y.

2 Lines Symmetry

Figure is symmetrical with only about two lines. The lines may be ver tical and horizontal lines as viewed in the letters H and X. Thus, we can see here two lines symmetry .

3 Lines Symmetry

An example of three lines of symmetry is an equilateral triangle. Here, the mirror line passes from the vertex to the opposite side dividing the triangle into two equal right triangles.

4 Lines Symmetry 

Four lines of symmetry can be seen in a square, that has all the sides equal. 

Infinite lines

Some figures have not one or two, but infinite lines passing through the centre, and the figure is still symmetrical. Example: a circle.

Lines of Symmetry for Different Shapes

Learn below the number of lines of symmetry for different shapes. 

• Lines Of Symmetry in a Parallelogram
• Lines of Symmetry in a Rectangle
• Rhombus Lines of Symmetry

Types of Symmetry

Symmetry may be viewed when you flip, slide or turn an object. There are four types of symmetry that can be observed in various situations, they are:

Translation Symmetry

Rotational symmetry.

• Reflection Symmetry

Glide Symmetry

If the object is translated or moved from one position to another, the same orientation in the forward and backward motion is called translational symmetry. In other words, it is defined as the sliding of an object about an axis. This can be observed clearly from the figure given below, where the shape is moved forward and backward in the same orientation by keeping the fixed axis.

When an object is rotated in a particular direction, around a point, then it is known as rotational symmetry or radial symmetry. Rotational symmetry existed when a shape turned, and the shape is identical to the origin. The angle of rotational symmetry is the smallest angle at which the figure can be rotated to coincide with itself. The order of symmetry is how the object coincides with itself when it is in rotation .

In geometry, many shapes consist of rotational symmetry. For example, the figures such as circle, square, rectangle have rotational symmetry. Rotational symmetry can also be found in nature, for instance, in the petals of a flower.

Below figure shows the rotational symmetry of a square along with the degree of rotation.

Click here for more information about rotational symmetry .

Reflexive Symmetry  

Reflection symmetry is a type of symmetry in which one half of the object reflects the other half of the object. It is also called mirror symmetry or line of symmetry. A classic example of reflection symmetry can be observed in nature, as represented in the below figure.

Read more about reflection symmetry here.

The combination of both translation and reflection transformations is defined as the glide reflection. A glide reflection is commutative in nature. If we change the combination’s order, it will not alter the output of the glide reflection.

Symmetrical Shapes

The symmetry of shapes can be identified whether it is a line of symmetry, reflection or rotational based on the appearance of the shape. 

The shapes can be regular or irregular. Based on their regularity, the shapes can have symmetry in different ways.  Also, it is possible that some shapes does not have symmetry. For example, a tree may or may not have symmetry.

These can be better understood with the examples given below.

Solved Examples

Example 1: If the figure below follows a reflexive or line of symmetry, then complete the figure.

Given that, the figure has a line of symmetry.

That means, the second half (i.e. missing part) of the figure will be exactly the same as the given.

Thus, the complete figure is:

Example 2: Identify the shapes which do not have rotational symmetry from the below figure.

As we know, rotational symmetry is a type of symmetry, when we rotate a shape in a particular direction, the resultant shape is exactly the same as the original shape.

Thus, from the given figure (a) and (c) do not have a rotational symmetry.

A number of other kinds of symmetric types exist such as the point, translational, glide reflectional, helical, etc. which are beyond the scope of learning at this stage.

Watch The Below Video To Know More About Symmetry and Types of Symmetry

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Frequently Asked Questions on Symmetry – FAQs

What is symmetry with example, what are the 4 types of symmetry, what is symmetric in math, why is symmetry in nature, can a line of symmetry be parallel.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Lines of symmetry

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Mirror images

A line of symmetry divides a figure into two mirror-image halves. In these geometry worksheets, students identify and draw lines of symmetry and symmetrical shapes .

Identify symmetrical shapes:

Lines of symmetry:

Draw symmetrical shapes:

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Balance and symmetry

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