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Are the two shapes congruent?
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In the picture, we can see two 2D shapes and we’re asked a simple yes-no question, “are they congruent?”
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To answer the question correctly, we’re going to need to remind ourselves what the word congruent means.
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Congruent shapes are exactly the same shape and exactly the same size.
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Now, we don’t need a ruler to compare the size of these shapes.
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Would you say they’re the same size?
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They’re not, are they?
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Just by looking at the shape on the right, we can see that it’s smaller.
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If our two shapes with the same shape, then they’d match exactly if one was put on top of the other.
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But take a moment and look at our shapes.
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Does it look like one would fit on top of the other?
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This is where the skill of being able to visualize shapes comes in useful.
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Imagine that we could take the shape on the right and move it across until it was on top of the shape on the left.
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Would it fit?
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No, it wouldn’t.
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We can see that the sides have matched up, but the base and the top part of our shape isn’t.
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What if we turned our shapes slightly?
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Would the two shapes match then?
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Not at all.
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We can tell just by looking at these two shapes, they’re not exactly the same shape and they’re not exactly the same size.
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The answer to this question is “no, these two shapes are not congruent.”