Line Symmetry

Lesson Objective

In this lesson, we will learn about line symmetry and what is line of symmetry.

About This Lesson

Looking at the picture on the right, we can see that the two sides of the picture are identical. Knowing this, we can say that this picture is symmetrical.

Now, we will learn about line symmetry and what is line of symmetry.

You can proceed by reading the study tips first or watch the math video or try out the practice questions.

$line symmetry for a fractal picture$

Study Tips

Tip #1

When we draw line across this equilateral triangle as shown in the picture, we can see that both sides of the triangle are the identical.

With this, this triangle is symmetrical along this line and this line is called line of symmetry.

The math video below will show you more on this visually.

Tip #2

Next, when we observe carefully, this equilateral triangle in fact has 3 lines of symmetry.

So next time, when you are given a shape to find all the lines of symmetry, be reminded to carefully analyze the shape carefully to avoid missing out any of these lines.

Now, watch the following math video to learn more.

Math Video

Click play to watch video

If the above player doesn't work, try this direct link.

Math Video Transcript

00:00:02.210
This is a lesson on line symmetry. 

00:00:07.010
Let's take a look at this picture. 

00:00:09.240
Now, when we draw a line across this picture, we will divide this picture into 2 sides.

00:00:16.230
Let's see what happens when we fold this picture along this line.

00:00:21.150
When folded, we can see that both sides of the picture are exactly the same.

00:00:27.040
When this happens, this picture is said to be symmetrical, and this line can be called the line of symmetry.

00:00:34.040
Next, let's try to fold this picture along this line.

00:00:38.200
Notice that, when we fold, both sides of the picture are not the same.  Therefore, this line is  
not the line of symmetry.

00:00:48.190
Let's try to fold along this line now. Again, both sides are not the same. Therefore, this line is not the line of symmetry.

00:01:00.110
Next, let's try to fold along this line. Again, both sides are not the same. Therefore, this line is not the line of symmetry.

00:01:13.240
With all these observations, we can see that this picture has only 1 line of symmetry.

00:01:21.160
Next, let's examine the line symmetry for this star.

00:01:26.050
Notice what happens, when we fold this star along this line.

00:01:30.220
When folded, we can see that side sides of the star, are exactly the same.

00:01:36.210
Hence, we can say that this star is symmetrical along this line.

00:01:42.240
How about this line? We can see that, this star is not symmetrical along this line.

00:01:51.100
Next, as for this line, we can see that, this star is symmetrical along this line.

00:01:59.000
Next, as for this line, we can see that, this star is not symmetrical along this line.

00:02:06.180
With some observations, we will notice that this star, has a total of 10 lines of symmetry.

00:02:14.240
Next, let's examine the line of symmetry for this ring.

00:02:19.190
When I fold this ring, we can see that this right is symmetrical along this line

00:02:25.110
The ring is also symmetrical, when it is folded along this line.

00:02:30.200
The observation is the same of this line.

00:02:36.000
Now, if we observe carefully, we will realize that this ring has infinite number of lines of symmetry.

00:02:43.040
Here, you can only see a few lines of symmetry, because I can not draw infinite number of them.

00:02:50.020
That is all for this lesson. Try out the practice question to further your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on line symmetry or pick your choice of question below.

Question 1 on finding the lines of symmetry of a five-pointed star
Question 2 on line symmetry of a parallelogram

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