# Lesson Video: Identifying Shapes With Symmetry Mathematics

In this video, we will learn how to decide whether a shape has a vertical line of symmetry.

06:08

### Video Transcript

Identifying Shapes with Symmetry

In this video, we will learn how to decide whether a shape has a line of symmetry.

Here’s a picture which has been folded in half. If we cut along the dotted lines and then unfold the shape, we end up with an aeroplane. The dotted line or the fold line can be called a line of symmetry. If we fold our plane along this line of symmetry, we know that both halves will be exactly the same shape. We can say that the aeroplane is symmetrical.

Is this star symmetrical? We can find out by folding the shape along the dotted line. We can cut around the outline and then open the shape up. The star is symmetrical.

This shape is symmetrical. We can see the line of symmetry. Let’s use the line of symmetry to help us complete the shape. Let’s start by drawing the line at the top. Starting from the line of symmetry, this line measures four squares. So, we need to draw four squares to the right. There we go. Now, we can do the same with the line at the bottom, four squares to the right. Now, we can complete the shape by joining this line. What shape do we have? It’s a rectangle. Rectangles have a line of symmetry.

Let’s complete this shape. The line at the bottom of this shape is about two squares long. Let’s try and draw it. There we go. Now, all we need to do is join up the rest of the shape. It’s a triangle. And it has a line of symmetry. This triangle is symmetrical. Finding out whether all triangles are symmetrical would make a great investigation.

Let’s try and complete this shape. The line at the top is about two squares long. So, starting at the line of symmetry, we can draw a line two squares long in the opposite direction. And we can do the same at the bottom. Now, all we need to do is join these two lines together. The completed shape is a square. The square is symmetrical. Because the square has equal sides, we can turn the square into different positions and still show the same line of symmetry.

Look closely at the dotted line drawn on the butterfly. Is it a line of symmetry? What would happen if we were to fold the butterfly along this line? It could look like this or like this. The dotted line is not the line of symmetry in this butterfly. Where should we draw the line of symmetry? This is the correct line of symmetry.

Let’s try some questions to practice identifying shapes with symmetry.

Does the following figure have a line of symmetry?

Is there a way we could fold this shape in half? Watch what happens if we fold the shape along this dotted line. Here’s one-half. Here’s the other half. And when we open it out, it looks like this. Does this figure have a line of symmetry? Yes, it does.

Does this figure have a line of symmetry?

Let’s try to fold the arrow along this line. If we were to cut out the shape, we’d be left with this. And if we were to open it out, we would get our arrow again. So, the line where we folded the arrow is the line of symmetry. Does this figure have a line of symmetry? Yes, it does.

Does the following figure have a line of symmetry?

We’re shown a shape. We have to work out if it has a line of symmetry. If you were to fold the shape in half to make each side equal, where would you fold it? Could this be the line of symmetry? If you were to place a mirror along this line of symmetry, this is what you’d see. This means that the shape is symmetrical. The answer to the question is yes, this figure does have a line of symmetry.

What have we learned in this video? We’ve learned how to identify shapes with symmetry.