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The Basics of Similarity


Oh, shapes, how do we compare thee? Let us count the ways.

1. You could be congruent.
2. You could be similar.
3. You could be totally unrelated.

Okay, that's enough.

Let's talk more about being similar. What does it mean for two shapes to be similar? Perhaps we can explain it with an analogy. We know what you're thinking: "Analogies? This is math, not English class." Tough noodles for you.

How about this? Congruence is to Popeye as similarity is to Wimpy. If congruence dined regularly on canned spinach, then similarity would gladly pay you Tuesday for a hamburger today.

In other words, similarity is a little weaker than congruence. We could say that congruent shapes have congruent angles and congruent sides. We could also say that pumpkin pie is a necessity on any Thanksgiving dinner table, but that's a given, so we won't waste our breath.

Similar shapes, on the other hand, have congruent angles, but proportional sides. That is, if we wrote ratios to compare the side lengths, the ratios would be equivalent.