# 9.20: Line of Symmetry

**At Grade**Created by: CK-12

**Practice**Lines of Symmetry

### Let's Think About It

Raven has been studying lines of symmetry with her class. When she goes home, she looks at her cat and notices that his face is symmetrical. She grabs a sheet of paper and holds it in the middle of her cat's face, then she rotates the paper to see if the cat's face has other lines of symmetry. What type(s) of line symmetry does Raven's cat have?

In this concept, you will learn about symmetry.

### Guidance

In geometry, a figure or an object can have **symmetry**. **Symmetry** is having one side that exactly mirrors the other.

Here is a butterfly. Notice that you can draw a line right down the center of the butterfly and one side will match the other side. Here is what that looks like.

When you can divide a figure or an object into two even matching halves, you say that the figure has **line symmetry**.

This figure can be divided in one way, vertically. If you tried to divide it horizontally, the two sides would not match.

Therefore, you can say that the butterfly has **bilateral symmetry**. Bilateral symmetry means that it has one line of symmetry that divides the butterfly in half.

A **line of symmetry** is a line that splits a figure into symmetrical parts. In the butterfly, there is one line of symmetry that can be drawn to show the two equal matching halves of the butterfly.

Let’s look at a picture of a figure that has more than one line of symmetry.

Here is a cross. This cross has four lines of symmetry. You can divide it vertically and horizontally and both sides will match. That shows two lines of symmetry.

There are other types of symmetry. There is **turn** or **rotational symmetry**. Rotational symmetry means that you can rotate the figure around a fixed point and it will look the same.

This star has rotational symmetry. It looks exactly the same no matter which point is rotated to be at the top. Since there are 5 points, this is a figure with a rotational symmetry of 5.

#### Guided Practice

Identify the lines of symmetry in the object.

First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?

Yes

Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?

No

Then, state the lines of symmetry.

Vertical

The answer is that the object has a vertical line of symmetry.

### Examples

Identify the lines of symmetry in each object.

#### Example 1

First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?

Yes

Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?

Yes

Then, state the lines of symmetry.

Vertical and horizontal

The answer is that the object has vertical and horizontal lines of symmetry.

#### Example 2

First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?

No

Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?

Yes

Then, state the lines of symmetry.

Horizontal

The answer is that the object has a horizontal line of symmetry.

#### Example 3

Yes

Next, draw lines from the middle of each side to the point opposite of it. Do both of the lines divide the object in halves that look the same?

Yes

Then, state the lines of symmetry.

One line of symmetry from each vertex to the middle of the opposite side for a total of three lines of symmetry.

The answer is that the shape has three lines of symmetry, one from each vertex to the middle of the opposite side.

### Follow Up

Remember Raven and her cat? Raven notices that her cat's face looks symmetrical. What type(s) of line symmetry does Raven's cat have?

First, draw a vertical line down the middle of the cat's face. Does the line divide the cat's face in to halves that look the same?

Yes

Next, draw a horizontal line down the middle of the cat's face. Does the line divide the cat's face in to halves that look the same?

No

Then, state the lines of symmetry.

Vertical

The answer is that the cat's face has a vertical line of symmetry.

### Video Review

### Explore More

Identify the lines of symmetry in each figure or object. Draw them in if possible.

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2.

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6.

Identify whether the following objects have rotational symmetry. If yes, write yes. If no, write no.

7.

8.

9.

10.

11.

12.

Find three other objects. Draw them and identify each line of symmetry. Share your findings with a friend.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.20.

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### Image Attributions

In this concept, you will learn about symmetry.