Video: Deciding If Two Given Shapes Are Congruent

Are the two shapes congruent?

01:33

Video Transcript

Are the two shapes congruent?

In the picture, we can see two 2D shapes and we’re asked a simple yes-no question, “are they congruent?” To answer the question correctly, we’re going to need to remind ourselves what the word congruent means. Congruent shapes are exactly the same shape and exactly the same size. Now, we don’t need a ruler to compare the size of these shapes. Would you say they’re the same size? They’re not, are they?

Just by looking at the shape on the right, we can see that it’s smaller. If our two shapes with the same shape, then they’d match exactly if one was put on top of the other. But take a moment and look at our shapes. Does it look like one would fit on top of the other? This is where the skill of being able to visualize shapes comes in useful. 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. Would it fit? No, it wouldn’t. We can see that the sides have matched up, but the base and the top part of our shape isn’t.

What if we turned our shapes slightly? Would the two shapes match then? Not at all. 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. The answer to this question is “no, these two shapes are not congruent.”

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