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Math Worksheets For All Ages

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Math Worksheets For All Ages

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Geometry Symmetry Worksheets

Symmetry in geometry refers to the concept of balance in an object, structure, and more often than not a geometric shape. It specifically refers to that when you flip, slide, or turn these things. If you can find two or parts of the object, structure or shape to be identical it exhibits symmetry. Reflection symmetry is the most common form of symmetry, this is when one side is a mirror or exact copy of the other side. You can often find lines of symmetry in shapes by folding them. If the folded parts fit directly on top of one another, each time you can do that, you have found a line of symmetry. These lessons and worksheets will teach you how to recognize lines of symmetry in a variety of objects.

Aligned Standard: 4.G.3

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

This section should help you master the concept of symmetry.

  • Qualify Homework 1 - If there is a line of symmetry, both sides of the line will be an exact mirror image of one another.
  • Draw Homework 2 - When we fold a shape in half and one half covers the other half, and we can say that the shape is symmetrical. And the fold line is the axis to see if it is the same on both sides.
  • Correct It Homework 3 - Imagine folding this picture along the dotted line. Answer: The two sides will not match up exactly. The dotted line is not the fixed half.

Practice Worksheets

Every different type of skill is broken into its own practice worksheets for you.

  • Practice 1 - The two sides match up exactly. Make sure that is true and fits the situation that you are exploring.
  • Practice 2 - Does the dashed line display symmetry? Write yes or no.
  • Practice 3 - Evaluate what see along the way and make sure that it fits the situation.

Math Skill Quizzes

It was really challenging to get all this work on to one single printed page! I hope it works for you.

  • Quiz 1 - As we know that symmetry is when one shape becomes exactly like another if you flip, slide or turn it.
  • Quiz 2 - Now we can see that there are some lines through which some images are not same. Ask yourself if you could fold the object directly onto itself and have it be equal.
  • Quiz 3 - After observing the figure we can see that dotted line is dividing into four equal parts. (Not sure what the line meant to say so I omitted it.

How to Find Symmetry of Objects

Symmetry with a Mirror on a Duck

A line of symmetry lies in every regular polygon object that you find in the environment. We can say that a symmetry is something that can create a perfect reflection or mirror image of an object by drawing an imaginary line. The line of symmetry is also defined as the imaginary line or the line of axis that goes through the center of the object or shape dividing it into perfect identical halves. There are only two types of geometric shapes that have no lines of symmetry, a scalene triangle (three unequal sides) and irregular quadrilaterals (parallelograms and trapezium). If an object changes when you flip, rotate it, or scale it is not symmetrical. An object that exhibits this is called asymmetrical.

Shapes and figures that are identical or have the exact resemblance to its other half, when they are divided into two or more equal portions are called symmetrical shapes. A great way to see if this is true with a three-dimensional object is to take a mirror and place it where you feel a line of symmetry may exist. See if the reflection is a direct match, if it is, it is a line of symmetry. If you slowly revolve the mirror around the object and evaluate it at each point, you will have a solid understanding if a line of symmetry does exist.

Let's try understanding this with the help of an example. Folding a figure or cutting it out from the center vertically can give us two identical halves. The two halves will be congruent to each other. The line from where the object will be cut or folded is the line of symmetry. Take a look at the duck, who happens to have a swim cap on. Do you see a line of symmetry in the reflection from the mirror?

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