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.”