Geometry For Dummies
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If you get a problem with a diagram of similar polygons that aren’t lined up in the same orientation, consider redrawing one of them so that they’re both aligned in the same way. This may make the problem easier to solve.

Here are a few things you can do to help you see how the vertices of similar polygons match up when the polygons are positioned differently:

  • You can often tell how the vertices correspond just by looking at the polygons, which is actually a pretty good way of seeing whether one polygon has been flipped over or spun around.

  • If the similarity is given to you and written out like


    you know that the first letters, J and T, correspond, K and U correspond, and L and V correspond. The order of the letters also tells you that segment KL corresponds to segment UV, and so on.

  • If you know the measures of the angles or which angles are congruent to which, that information tells you how the vertices correspond because corresponding angles in similar polygons are congruent.

  • If you’re given (or you figure out) which sides are proportional, that info tells you how the sides would stack up, and from that you can see how the vertices correspond.

About This Article

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About the book author:

Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses and standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. Ryan is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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