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Properties of Similar Polygons - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio (in other words, if they are proportional). Typically, problems with similar polygons ask for missing sides. To solve for a missing length, find two corresponding sides whose lengths are known. After we do this, we set the ratio equal to the ratio of the missing length and its corresponding side and solve for the variable.

If two figures are congruent, then we said that all corresponding sides and all corresponding angles must also be congruent. Which means they're basically the same figure and exactly the same size. If we're talking about similar figures, what we're talking about shapes that are the same but not necessarily the same size. That's not very precise. So there are two key things for figures to be similar.
The first first thing is that corresponding blank must be congruent. Well if we look at these two figures and let's say they're similar, we can see that the sides that correspond are definitely not going to be congruent. So the corresponding angles must be congruent.
Secondly, and again it has to be both of these for them to be similar. Corresponding sides must be proportional. So what that means is if I said that these two figures were similar, that is if a, b, c, d, e and I'm going to write that over here. If a, b , c, d, e pentagon and this figure f, g, h, I, j, g, h, i, j are similar, notice it kind of looks like a congruence marking except for we do not have the equal sign. So if you just have Mr. Squiggles all by himself, then that means that they're similar. So what that means is that the ratio of ab:fg is the same as bc:gh of cd:hi and so on.
So the way that you check if two figures are similar corresponding angles must be exactly the same, they must be congruent, and the corresponding sides must be proportional.

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