Lesson Video: Lines of Symmetry Mathematics • 4th Grade

In this video, we will learn how to draw lines of symmetry in shapes and figures and count all the lines of symmetry in given shapes.

07:50

Video Transcript

Lines of Symmetry

In this video, we’re going to learn how to draw lines of symmetry in shapes and figures and count all the lines of symmetry in given shapes. If we look around us, we can see lots of examples of symmetry in real life. This leaf is symmetrical and this is where we would draw the line of symmetry. If we were to fold the leaf in half along the line of symmetry, it would look like this and the other half would look like this. And if we flip this leaf over like so, we could place one-half of the leaf on top of the other and they would be a complete match. This is how we know the leaf is symmetrical.

Where would you draw the line of symmetry on this picture of a crab? You should go here. Sometimes people call the line of symmetry a mirror line because each half is a mirror image of the other half. If we were to place a mirror on this line of symmetry, the reflection would look like this. This is another way to tell if a shape is symmetrical. Some shapes are symmetrical like this rectangle, and this is its line of symmetry. If we rotate or turn this rectangle, we can see another line of symmetry. Some shapes have more than one line of symmetry. This rectangle has two.

How many lines of symmetry does this triangle have? We’ve drawn one line of symmetry from the vertex at the top of the triangle down through the middle of the shape. And if we turn or rotate the triangle, we could draw another line of symmetry from the vertex at the top of the triangle through the middle of the shape like so. So far, we found two lines of symmetry. If we rotate the triangle again, we could draw another line of symmetry. Starting at the vertex at the top, again, we can draw a line all the way through the middle of the triangle, so this equilateral triangle has three lines of symmetry.

So far, we’ve learned how to draw lines of symmetry onto shapes or figures and how to count the number of lines of symmetry a shape or figure has. Let’s try some questions now and put into practice what we’ve learned.

Which of these are lines of symmetry of the letter? Line A only, lines A and C, line B only, lines A and B, or line C only.

In this question, we’re shown a capital letter A and it has three lines drawn on it, lines A, B, and C. We have to decide which of these lines are lines of symmetry of the letter A. Let’s start by looking at line A. Is this line a line of symmetry? One way we could find out is to think about what would happen if we folded this letter along line A. One-half would look like this, and the other half would look like this. We couldn’t fit each half on top of each other and make a match. So line A is not a line of symmetry. So we can eliminate line A as a possible answer and any of the possible answers which have line A in them.

What about line B? Is this a line of symmetry? If we were to fold along the line B, each half would look like this. We can’t fit one-half on top of the other. And if we were to place a mirror line along line B, we end up with a very funny-looking letter. Line B is not a line of symmetry either. So line C must be the one which is a line of symmetry. Let’s check. If we fold along the line of symmetry, one-half of the letter A would look like this and the other half would look like this. If we were to flip this half over like so, we could fit it perfectly on top of the other half like so. This is how we know that line C is a line of symmetry. So the correct answer is line C only. This is the only one of the three lines which is a line of symmetry of the capital letter A.

How many lines of symmetry does this figure have?

In this question, we’re shown this star figure, and we’re asked to work out how many lines of symmetry it has. We could start from this vertex here at the top of the star and draw a line of symmetry cutting through the middle of the star like so. If we were to place a mirror along this line of symmetry, the reflection would look like this. This is how we know this shape is symmetrical and the line is a line of symmetry. So far, we found one line of symmetry in the star shape. If we turn or rotate the star so that one of the points is pointing upwards, we could draw another line of symmetry going through the middle of the shape, just like before.

So far, we’ve found two lines of symmetry. In the same way, we can rotate or turn the star and draw another line of symmetry. We’ve found three lines of symmetry. By turning the shape again, we can draw a fourth line of symmetry. And if we turn the shape one more time, we can draw another line of symmetry. Altogether, we counted five lines of symmetry. By starting at the top point each time and drawing a line down through the middle of the shape, we were able to draw five lines of symmetry. This star shape has five lines of symmetry.

What have we learned in this video? We’ve learned how to draw lines of symmetry in shapes or figures. We also learned how to count the lines of symmetry in given shapes or figures.

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