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Question Video: Determining Which of Given Shapes Is Not Congruent to the Others Mathematics

Which shape is not congruent to the others?


Video Transcript

Which shape is not congruent to the others?

This problem is a sort of odd-one-out question. We’re given some shapes and we need to find the one that’s different. This is because when shapes are congruent, we know they’re exactly the same size; they’re exactly the same shape. So, four out of our five shapes are exactly the same size and shape. But one of them is not congruent. We’re looking then for the shape that’s different.

Now, as we’ve just said, there are two parts, two shapes, being congruent. They must be the same size, and they must be exactly the same shape. It doesn’t matter what color they are; it doesn’t matter what position we put them in. But those two factors must be true. Now, if we look at our five shapes, we can see that they’re all in different positions. As we’ve just said, this doesn’t mean they can’t be congruent. We know that two shapes can be exactly the same, but just in a different position. But it does make them harder to spot.

One way that we could check which of these shapes are the same even though they’re in different positions would be to put a little piece of tracing paper or some sort of paper we can see through over one of the shapes then trace it and then move it to see if it fits exactly on top of any of the other shapes. For example, we’ve just proved that shapes (a) and (d) are congruent.

But you know, perhaps there’s a quicker way to find the answer here, because not only the shapes need to be exactly the same shape to be congruent, they need to be exactly the same size. And one of these shapes is not the same size as any of the others. We don’t need to get a ruler or anything like that. We can see just by looking with our eyes that shape (b) is larger than any of the other shapes. So, although we could go from (a) to (e) and check whether they’re exactly the same shape, perhaps using tracing paper, we’ve identified what we could call the odd one out because it’s not the same size as any of the others. The shape that is not congruent is shape (b).

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