Question Video: Identifying Vertical and Horizontal Lines of Symmetry Mathematics

True or false: The given shape has a vertical line of symmetry.

02:13

Video Transcript

True or false: The given shape has a vertical line of symmetry.

In this question, we’re given a statement and we need to decide whether it’s correct or not. Underneath the statement, we’re given a picture of a shape. This is the shape that the statement is talking about. Now, did you notice the words “line of symmetry” in the question? Do you remember what a line of symmetry is? If we know that a shape or an object has a line of symmetry, we can think of it like a line or a fold through the middle of the shape. And if that shape is symmetrical, then if it were folded, both sides would fit perfectly on top of each other.

We can also think of symmetry in terms of reflection. We know that a shape or a picture has symmetry when we can take half of the shape and see that it reflects perfectly across the line of symmetry and still looks the same. And as we can see from these little pictures, lines of symmetry can go in all sorts of directions. But our question only talks about one type of line. The given shape has a vertical line of symmetry.

Now, we know that a vertical line is a line that goes up and down. It doesn’t slope to the sides at all. It’s perfectly straight from top to bottom. So, can we draw a line straight up and down from top to bottom somewhere on this shape so that it becomes a line of symmetry?

Well, we know that for lines of symmetry to work, they need to run through the middle of objects. So, if we can find the middle of this shape, which is here, and then draw a perfectly vertical line. What do you think? Is this a line of symmetry? If we folded this shape across the dotted line, do you think one side would fold perfectly on top of the other? If we put a mirror along the dotted line, do you think we’d see that one side is a reflection of the other? I think we would, wouldn’t we?

The line of symmetry in this shape doesn’t run horizontally from side to side and is not sloped in any way. But we can see that the shape has a vertical line of symmetry. The statement in the question is true.

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