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Lines of Symmetry Worksheets

4.G.3
Answer Keys Here

Aligned To Common Core Standard:

Grade 4 Geometry - 4.G.3

How to Identify Lines of Symmetry in Two-Dimensional Figures - A line of symmetry is a hypothetical or virtual line that divides a figure into two identical patterns or shapes. One of the most common ways of finding the line of symmetry is through a folding test. When a shape is folded, and it sits perfectly on top, i.e., matching all edges, then the fold line is called the line of symmetry. Here is a rectangle folded one way which didn't work Here is another way that did work and matched all the edges perfectly, making the line of symmetry. Triangles - Triangles can have more than one line of symmetry, which can be seen in the figure below. The first figure is the equilateral triangle in which all the sides of the triangle are equal, which makes it easier to make more than one line of symmetry. The second figure is the isosceles triangle, where only two sides are equal, and therefore, it was only possible to make one line of symmetry. The last figure is the scalene triangle in which it was impossible to find a single line of symmetry as none of the sides or angles are equal in this case. This worksheet and lesson series will help students learn to identify lines of symmetry between several geometric figures.

Printable Worksheets And Lessons


  • Step-by-Step Lesson- We tackle this concept head on. I always tell people, if it can fold on top evenly, it's asymmetrical.

  • Guided Lesson - We again ask you if a drawn line shows symmetry, but we also have you draw your own lines.

  • Guided Lesson Explanation - The answer keys are tricky when you have kids drawing their own lines. There are a lot of correct answers; I guess there are many wrong answers, too.

  • Practice Worksheet - This is in a "bubble" this-and-that testing format. That is usually how you will see these types of questions.

  • Matching Worksheet - Match shapes to a slice of their symmetrical ends. I never saw this before, just thought it was a fun way to do it.


  • Transformation - Worksheet Five-Pack - We look at the orientation of these objects and where they are caught at. Left to right or top to bottom?

  • Read the Lines Worksheet Five Pack - Once again, left, right, top, or bottom. Where can you find that mathcing side?






Homework Sheets

I tried to cover this concept from every angle that I could; isn't that ironic?




Practice Worksheets

You will decide not only how many lines of symmetry there are, but if you can qualify pre-drawn lines.

  • Practice 1 - The lines are pre-drawn to provide you with guidelines. See how you make out with these.
  • Practice 2 - Does the dashed display line symmetry? Write yes or no. For extra credit explain why.
  • Practice 3 - Draw the lines on all of these shapes to display a level of balance.



Math Skill Quizzes

These are some of the most interesting quizzes that I have ever created.

  • Counting Quiz 1 - How many lines of symmetry does each figure have? These are some pretty cool figures to work with.
  • Reflections Quiz 2 - Draw the other half to match. This quiz is asking you what is missing.
  • Defined Quiz 3 - Are the lines correct? Some are and then again, some are not.


Why Is Identifying Symmetry Important?

Being able to identify a balanced system is helpful in many different applications. It as equally important as being able to identify asymmetry or imbalance found within a system. While many people think that this is a math skill while in fact it is life skill that will serve you well in many different walks of life. Symmetry is a foundational concept in geometry and helps us understand shapes, figures, and structures in many different technical aspects. There are times when you will want to shift a stable system to a less stable system. Maybe you need to redistribute supplies, maybe you need to bring more stability to another system by making another system less stable. Either way it all starts with being able to identify a system that is balanced and find signs of asymmetry within that system.