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How can you create a copy that is similar (but not congruent) to the original?

If you pursue any career that requires drawing--artist, designer, engineer, or architect--you will need to draw something "to scale" at some point. That is, you'll need to create a smaller or larger version of an image that is similar to the original, but not so similar that the images are congruent.

You've practiced identifying simple shapes that are similar. Now see if you can identify similarities between two more detailed images.

Here is a sketch of a bunny.

Which of the sketches below is a good reproduction of the first bunny? Click on the image that is most similar to the original sketch. Then try to explain how you made your decision.

Skinny and tall rabbit. Short and wide rabbit. Normal rabbit.

Question

Did you choose the right drawing? How did you make your decision?

There are a few ways to choose the best drawing. One way to tell you whether a picture is distorted is to compare the ratio of length to height. Another way would be to compare angles; although, it is not so easy to measure angles in the bunny sketches. You could go to great lengths and draw the original using a scale drawing technique on graph paper. In fact, a good way to think of "similarity" is to think of scale drawings. Any objects similar to each other are scaled copies of each other. Fortunately for us, the drawings in geometry will not take as long to draw as this bunny did!

Question

Which bunny was drawn to scale? How could you tell?

If you thought that the first two images were distorted and the third bunny was drawn to scale, you're right! You may have arrived at this conclusion by comparing ratios of length to height between the images.

Another way to identify an accurately scaled drawing is to measure the angles in the original and compare those measurements to the angles in the copy. (Of course, bunny sketches do not really have angles.)

Question

What does geometric similarity have to do with scaled drawings?

Objects that are similar to each other are scaled copies of each other.