Video: Finding the Missing Shape in a Symmetrical Pattern

This pattern is symmetrical. What shape is missing?

02:19

Video Transcript

This pattern is symmetrical. What shape is missing?

If we’re given a repeating shape pattern, we often look at it from left to right, and we notice part of the pattern that keeps repeating itself. But if we look at this pattern from left to right, we can’t see any parts that are repeated again and again. That’s because this isn’t a repeating pattern. Instead, we’re told that this pattern is symmetrical. What does it mean for something to be symmetrical?

We know that for something to be symmetrical, we can draw a line through the middle of it and it will be the same on both sides. Now, for a pattern to be symmetrical, it must also be the same on both sides. But where’s the middle of our pattern? Where could we draw a line where the pattern is the same on both sides? Can you see where we could draw our line? This wouldn’t be right, would it? On one side of the line, we’d have a green rectangle and on the other side, a yellow square. This isn’t a line of symmetry.

This looks more like it. On both sides of the line, we can see a yellow square. And as we move outwards, the pattern changes in exactly the same way. We then have two green rectangles. Now, we can see on the right-hand side of our pattern, there’s a missing shape. But we can use our knowledge of symmetry and how the pattern changes to work out what this missing shape is.

Can you see what it’s going to be? After the green rectangles come the blue triangles, only we haven’t got a blue triangle on the right-hand side, have we? But as soon as we sketch it on, we can see that our pattern now looks symmetrical. We found the center line of our pattern, and we made sure that it looked the same on both sides of this line. Our missing shape is a blue triangle.

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